# A researcher is interested in

A researcher is interested in testing whether  annual house hold income in Philadelphia is normal. So she took a sample of 50 house holds and found that skewness  (s)= 2.3190 and Kurtosis (k) = 6.7322. Use the Jarque- Bera Test to test , at alpha 0.05, whether income follows normal distribution.

-Yes, population is normal because Chi-Square test is higher than critical value.

-Yes, population is normal because Chi-Square test is less than critical value.

-No, population is not  normal because Chi-Square test is higher than critical value.

-No, population is not  normal because Chi-Square test is less than critical value.

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the estimated standard error?

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the effect size (Cohen’s d)?

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the effect size  (r2) ?

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the effect size  (r2) ?

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the alternative hypothesis

# A researcher is interested in

A researcher is interested in hamster wheel-running activity during the summer versus the winter. He suspects that either the hamsters will run less during the winter to conserve energy or they will run more to keep warm. He records the activity of n = 16 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February.
The data are collected, and the results show an average difference score of MDD = 3.8 and a sum of squares of SS = 522.15.
What is the value for degrees of freedom for this repeated-measures t test?
47

15

50

16

What is the sample standard deviation (s) for the D scores?
1.48

5.9

522.15

34.81

What is the estimated standard error of the mean difference (sMDMD) for this study?
0.37

2.18

1.48

1.22

# A researcher is interested in

1. A researcher is interested in the effect of positive affirmations on self-confidence. What is the consequence of adding gender as a factor in the ANOVA?
 a. The MSwithin treatments value will increase. b. The MSwithin treatments value will decrease. c. The MSbetween treatments value will increase. d. The MSbetween treatments value will decrease.

2. Which statement below is not consistent with the benefits of adding an individual difference variable (i.e., gender) to a single factor (i.e., factor A) ANOVA?
 a. doing so reduces the within treatments variance b. doing so allows for examination of whether there are differences between the levels of the individual difference variable c. doing so reduces the between treatments variance for the single factor d. doing so reveals if an interaction exists between the individual difference variable and the single factor

3.The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. Which value for the missing mean would most clearly result in a main effect for factor A?

B1   B2

 ​ A1 ​ 20 ​ 40 ​ A2 ​ 50 ​ ?

 a. M = 40 b. M = 30 c. M = 10 d. M = 20

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the critical/cut-off t-value with an alpha level of .05 (two-tailed)?

# A researcher is interested in

A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes.

 Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37

Using symbols, state the hypotheses for a two-tailed test with α=0.05.

Locate the critical region. In doing so, determine the degrees of freedom values.

Calculate the F-ratio.

State the conclusion of these findings.

# A researcher is interested in

A researcher is interested in the relationship between birth order and personality. A sample of n = 100 participants is obtained, all of whom grew up in families as one of three children. Each participant is given a personality test, and the researcher also records the person’s birth-order position (1st, 2nd, or 3rd born). The frequencies from this research study are shown in the following table.

Calculate Cramér’s V as a measure of effect size.

Birth Position

1st   2nd   3rd

 ​ Outgoing ​ 13 ​ 31 ​ 16 ​ Reserved ​ 17 ​ 19 ​ 4

# A researcher is interested in

(Continuing from the last question, with the same values)

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you computed the estimated standard error (sM)

For this question, compute the value of the t-test. t =?

# A researcher is interested in

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you provided the degrees of freedom

# A researcher is interested in

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

What is the effect size (Cohen’s d) for the difference?

# A researcher is interested in

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

Compute the sample variance s2=  ?

AND WRITE THAT NUMBER DOWN. YOU WILL NEED IT FOR THE NEXT QUESTION

# A researcher is interested in

A researcher is interested in seeing the relationship between the number of hours slept and mood. Mood was measured on a scale from 1-5, with higher scores indicating happier mood.

 Hours Slept (X) Mood (Y) 5 2 7 4 8 5 6 3 6 2 10 4

a) What is the slope of the regression equation?

b) Find the y-intercept.

c) What is the expected mood for someone who got 8 hours of sleep.

d) What is the error between the actual mood of someone who got 8 hours of sleep and their expected mood?

# a. What are your conclusions and observations about the relationship between the two variables

b.What is the value of the intercept a?

c. What is the value of the slope b?

d. Write the linear regression equation

# A researcher is interested in

A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 112 students who averaged 26.7 texts per day. The standard deviation was 24.5 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a     distribution.

b. With 95% confidence the population mean number of texts per day is between  and   texts.

c. If many groups of 112 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in the relationship between birth order and personality (outgoing versus reserved). A sample of n = 100 people is obtained, all of whom grew up in families as one of three children. Each person is given a personality test, and the researcher also records the person’s birth-order position (1st born, 2nd, or 3rd). The frequencies from this study are shown in the following table. On the basis of these data, can the researcher conclude that there is a significant relation between birth order and personality? Test at the .05 level of significance.

 1st 2nd 3rd Outgoing 13 31 16 Reserved 17 19 4

# A researcher is interested in

1. A researcher is interested in the relationship between cigarette smoking and BMI (kg/m2) in adolescents. In order to test his hypothesis, the researcher decides to divide cigarette smoking into four groups based on the number of cigarettes smoked per day versus a control group of never smokers. The following incomplete ANOVA table summarizes a preliminary analysis for the difference in mean BMI for the groups.

 Sum of Squares df Mean Square Between Groups 54 Within Groups 38 Total 197
1. Fill in the ANOVA table above for all missing values.

1. B) Calculate your F statistic for the one way analysis of variance.

# A researcher is interested in

A researcher is interested in gender differences in attitudes toward dating. Specifically, she wants to test the hypothesis that women are more accepting than men are of the idea that men should always pay on the first date, and thus women should have a more traditional view of dating than men do. Data are collected from 10 women and 10 men using a scale that measures dating behaviors and attitudes. Higher scores mean more traditional dating attitudes. Answer the following:

1) What are the independent and dependent variables in this study?

2) What inferential statistic discussed thus far could be used to answer this question?

# A researcher is interested in

A researcher is interested in learning whether young people whose fathers are absent from home are more likely to engage in delinquent behaviours. She compares the arrest rates of boys whose fathers are absent with those of boys whose fathers are present at home across socio economic status (e.g., lower SES, middle SES, upper SES). What type of data is the researcher collecting?
Select one:
A.

archived data
B.

self-report data
C.

case study data
D.

experimental data
E.

naturalistic observation

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 95 students who averaged 26.3 texts per day. The standard deviation was 21.4 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t  distribution.

b. With 98% confidence the population mean number of texts per day is between_____  and _____   texts.

c. If many groups of 95 randomly selected members are studied, then a different confidence interval would be produced from each group. About________  percent of these confidence intervals will contain the true population number of texts per day and about ______  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in seeing if the average income of rural families is greater than that of urban families. To see if his claim is correct he randomly selects 35 families from a rural area and finds that they have an average income of \$65210 with a population standard deviation of \$891. He then selects 59 families from a urban area and finds that they have an average income of \$69285 with a population standard deviation of \$616. Perform a hypothesis test using a significance level of 0.05 to test his claim. Let rural families be sample 1 and urban familis be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.05 the critical value is 1.645

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that the average income of rural families is greater than that of urban families.
• There is not enough evidence to reject the claim that the average income of rural families is greater than that of urban families.
• There is enough evidence to support the claim that the average income of rural families is greater than that of urban families.
• There is not enough evidence to support the claim that the average income of rural families is greater than that of urban families.

# Using the data in the above table, provide the following information:

a. interpret the coefficient of determination

b. What is the p-value?

# A researcher is interested in

A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes.

 Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37

Using symbols, state the hypotheses for a two-tailed test with α=0.05.

Locate the critical region. In doing so, determine the degrees of freedom values.

Calculate the F-ratio.

State the conclusion of these findings.

# A researcher is interested in

• A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes.

 Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37

A. Using symbols, state the hypotheses for a two-tailed test with α=0.05.

B. Locate the critical region. In doing so, determine the degrees of freedom values.

# A researcher is interested in

A researcher is interested in the relationship between birth order and personality. A sample of n = 100 participants is obtained, all of whom grew up in families as one of three children. Each participant is given a personality test, and the researcher also records the person’s birth-order position (1st, 2nd, or 3rd born). The frequencies from this research study are shown in the following table.

A. Should the researcher conclude that there is a significant relation between birth order and personality? Use α = .05.

B. Calculate Cramér’s V as a measure of effect size.

Birth Position

1st   2nd   3rd

 ​ Outgoing ​ 13 ​ 31 ​ 16 ​ Reserved ​ 17 ​ 19 ​ 4

# A researcher is interested in

A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 104 students who averaged 45.1 texts per day. The standard deviation was 12.8 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval , (which one should be used t or z)   distribution.

b. With 95% confidence the population mean number of texts per day is between  and   texts.

c. If many groups of 104 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population number of texts per day and about  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in the effectiveness of a new medication at reducing systolic blood pressure via a new medication in a group of hypertensive patients. The medication has entered the phase II period for clinical trials, and the researcher has determined three doses to test on his participants. Suppose the following ANOVA table summarizes the findings of the study with respect to the four groups (three different doses and one control).
Between Groups Within Groups Total
Sum of Squares df 2267.6 3 1478.2 50 3745.8 53
Mean Square 755.87 29.564
A) Write out your null and alternative hypotheses for a one way analysis of variance.
B) Assume all conditions for such a procedure are met. Calculate an F statistic and a pvalue for the procedure and determine if there is a difference between the groups.

# A researcher is interested in

A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 140 students who averaged 35.2 texts per day. The standard deviation was 18.8 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean number of texts per day is between  and   texts.

c. If many groups of 140 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population number of texts per day and about  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 135 students who averaged 38.6 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.6 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t  distribution.

b. With 95% confidence the population mean minutes of concentration is between  and   minutes.

c. If many groups of 135 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean minutes of concentration and about  percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the null hypothesis

# A researcher is interested in

A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 2323 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500500-mg supplement of calcium each day. Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 15.8 pounds with a standard deviation of 1.9 pounds. The members of Group B had lost a mean of 16.6 pounds with a standard deviation of 1.4 pounds during the same time period. Assume that the population variances are not the same. Construct a 99% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500-mg supplement of calcium each day, and let Population 2 be the amount of weight lost by Group B, who did not take a calcium supplement. Round the endpoints of the interval to one decimal place, if necessary.

# A researcher is interested in

A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 100 students who averaged 41.2 texts per day. The standard deviation was 15.3 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z or t  distribution.

b. With 90% confidence the population mean number of texts per day is between          and         texts.

c. If many groups of 100 randomly selected members are studied, then a different confidence interval would be produced from each group. About    percent of these confidence intervals will contain the true population number of texts per day and about          percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 123 students who averaged 34.9 texts per day. The standard deviation was 12.2 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t or z  distribution.

b. With 98% confidence the population mean number of texts per day is between  and   texts.

c. If many groups of 123 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population number of texts per day and about  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in whether there is a difference between male and female college students in the amount of time spent doing volunteer work for the last 6 months. The researcher gathers a random sample of college students. The amount of time volunteering is measured in hours, which is an interval level-ratio and is normally distributed. Which statistical test should be used to analyze this data?
a.

Multiple regression
b.

paired samples t-test
c.

independent groups t-test
d.

Factorial ANOVA

# A researcher is interested in

A researcher is interested in examining the relationship between assertiveness and level of stress in college students. She believes that college students who are more assertive experience less stress than students who less assertive. She surveys a random sample of college students and asks them to complete a questionnaire in which they rate their level of assertiveness and level of stress on a 5-point scale. Answer the following questions:

1) What are the scales of measurement for level of stress and assertiveness?

2) Which inferential statistics should be used to solve this complex research problem?

# A researcher is interested in

A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 149 students who averaged 39.2 texts per day. The standard deviation was 24.2 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t or z  distribution.

b. With 90% confidence the population mean number of texts per day is between___  and ____  texts.

c. If many groups of 149 randomly selected members are studied, then a different confidence interval would be produced from each group. About 90% percent of these confidence intervals will contain the true population number of texts per day and about ____ percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 124 students who averaged 39.8 minutes concentrating on their professor during the hour lecture. The standard deviation was 12.9 minutes.Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z distribution.

b. With 98% confidence the population mean minutes of concentration is between  and   minutes.

c. If many groups of 124 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in whether participat-ing in sports positively influences self-esteem in young girls. She identifies a group of girls who have not played sports before but are now plan-ning to begin participating in organized sports. The researcher gives them a 50-item self-esteem inventory before they begin playing sports and administers the same test again after 6 months of playing sports. The self-esteem inventory is measured on an interval scale, with higher num-bers indicating higher self-esteem. In addition, scores on the inventory are normally distributed. The scores follow:

Before:

44

40

39

46

42

43

After:

46

41

41

47

43

45

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute and interpret the effect size.

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 96 students who averaged 38.7 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.2 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t distribution.

b. With 98% confidence the population mean minutes of concentration is between  and   minutes.

c. If many groups of 96 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 120 students who averaged 39.7 texts per day. The standard deviation was 13.8 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z or t  distribution.

b. With 95% confidence the population mean number of texts per day is between      and      texts.

c. If many groups of 120 randomly selected members are studied, then a different confidence interval would be produced from each group. About                    percent of these confidence intervals will contain the true population number of texts per day and about             percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 95 students who averaged 26.9 texts per day. The standard deviation was 22.1 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z or t  distribution.

b. With 98% confidence the population mean number of texts per day is between     and       texts.

c. If many groups of 95 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population number of texts per day and about  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

A researcher is interested in whether a new antidepressant drug D has an effect on people’s self-rating of depression. She randomly assigns 12 people into two groups so that each group has 6 people. One group is given drug D daily, and the other group is not given drug D. Call these the Drug group and the No Drug group, respectively. After one month of treatment, all 12 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data:

Drug     No Drug
2        4
3        5
4        5
4        4
2        6
3        6
nD = 6 nND = 6
MD = 3 MND = 5
sD = 0.89 sND = 0.89

Using an α-level of .05, perform a two-tailed t-test to determine whether there was an effect of Drug D on depression ratings. Specifically, answer the following questions:

1. What is the total degrees of freedom for this problem?
2. Calculate the standard error of the difference between sample means.
3. Calculate the t-score for the difference between sample means, MD-MND
4. Using Table T, what is the critical value of t for this problem?
5. Based on the relationship between the value of t you calculated in (3) and the critical value of t from (4), can the researcher conclude that there is an effect of Drug D on on depression ratings?

# A researcher is interested in

A researcher is interested in examining the effects of relaxation techniques on test performance. The researcher randomly selects thirty college students and randomly assigns them into two groups of fifteen each.  One group receives training in several relaxation techniques and the second group receives no training. Each group is given a statistics test.  The average score for the group that received the relaxation training was 75 (s² = 5) and the average for students who did not receive the relaxation training was 50 (s² = 8). (1) State the null and alternative hypotheses for this study (2) What is the dependent and independent variable for this study (3) What test statistic/hypothesis test would you select to determine if the means are significantly difference at the alpha .05 level? (4) What critical value would you use to make your decision to reject or retain the null hypothesis at alpha .05?

# A researcher is interested in

A researcher is interested in infants’ attention to their mothers’ voices. The research wants to know if the infant’s attention increases to the mother’s voice after spending the first week of life with the mother. The researcher selects 10 full-term infants with normal health who experienced uncomplicated deliveries and tested the number of seconds that the infant oriented in the direction of the mother’s voice on Day 1 and on Day 7 after delivery. These fictional data appear below. Use an α = 0.01

Day 1 Day 7
6 7
5 7
3 6
8 8
7 9
6 8
5 5
6 8
8 7
5 8

# A researcher is interested in

question 17

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 108 students who averaged 34.3 texts per day. The standard deviation was 13.7 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z or t  distribution?

b. With 98% confidence the population mean number of texts per day is between ____ and___texts.

c. If many groups of 108 randomly selected members are studied, then a different confidence interval would be produced from each group. About____  percent of these confidence intervals will contain the true population number of texts per day and about______  percent will not contain the true population mean number of texts per day.

# A researcher is interested in

• A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes.

 Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37

a. Using symbols, state the hypotheses for a two-tailed test with α=0.05.

b. Locate the critical region. In doing so, determine the degrees of freedom values.

c. Calculate the F-ratio.

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 103 students who averaged 32.7 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.4 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 98% confidence the population mean minutes of concentration is between _____and  _____ minutes.

c. If many groups of 103 randomly selected members are studied, then a different confidence interval would be produced from each group. About _______percent of these confidence intervals will contain the true population mean minutes of concentration and about ________ percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the critical/cut-off t-value with an alpha level of .05 (two-tailed)?

 -2.120 ±2.120 -2.131 ±2.131

# A researcher is interested in

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 96 students who averaged 40.3 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.5 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a  z or t  distribution.

b. With 98% confidence the population mean minutes of concentration is between _____  and ______   minutes.

c. If many groups of 96 randomly selected members are studied, then a different confidence interval would be produced from each group. About _____ percent of these confidence intervals will contain the true population mean minutes of concentration and about ______  percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

Compute the sample variance s2=  ?

AND WRITE THAT NUMBER DOWN. YOU WILL NEED IT FOR THE NEXT QUESTION

# A researcher is interested in

(Continuing from the last question, with the same values)

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you computed the sample variance (s2)

For this question, compute the estimated standard error (sM) = ?

AND WRITE THAT NUMBER DOWN. YOU WILL NEED IT FOR THE NEXT QUESTION

# A researcher is interested in

Continuing from the last question, with the same values)

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you computed the estimated standard error (sM)

For this question, compute the value of the t-test. t = ?

AND WRITE THAT NUMBER DOWN. YOU WILL NEED IT FOR THE NEXT QUESTION

# A researcher is interested in

(Continuing from the last question, with the same values)

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you provided the degrees of freedom

 Yes, the value of the t-test exceeded the critical value of +/- 1.711 No, the value of the t-test did not exceed the critical value of +/- 1.96 Yes, the value of the t-test exceeded the critical value of +/- 2.064 No, the value of the t-test did not exceed the critical value of +/- 0.685

# A researcher is interested in

(Continuing from the last question, with the same values)

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you computed the value of the t-test

For this question, answer, how many degrees of freedom does this t-test have?

AND WRITE THAT NUMBER DOWN. YOU WILL NEED IT FOR THE NEXT QUESTION

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the null hypothesis?

 H0: µchocolate > µno-chocolate H0: µchocolate < µno-chocolate H0: µchocolate = µno-chocolate H0: µchocolate + µno-chocolate

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

What is the alternative hypothesis?

 Ha: µchocolate > µno-chocolate Ha: µchocolate < µno-chocolate Ha: µchocolate = µno-chocolate Ha: µchocolate ≠ µno-chocolate

# A researcher is interested in

Question 2: A researcher is interested in the correlation between the height (in inches) and weight (in pounds) of males. The researcher measured the height and weight of four males. The measured values are

 Participant Height Weight Participant 1 70 160 Participant 2 69 164 Participant 3 61 134 Participant 4 66 155 Participant 5 71 170 Participant 6 65 158 Participant 7 67 160 Participant 8 73 180 Participant 9 67 165 Participant10 64 146

1) Plot the scatterplot to show the relationship between height and weight, label the value for each participant.

2) Base on the scatterplot, describe the relationship between height and weight (form, direction, strength, possible outlier)?

3) Calculate the correlation coefficients. Does it confirm your judgment in the previous question?

# A researcher is interested in

A researcher is interested in testing whether chocolate causes hyperactivity in children. To test this hypothesis, researcher recruits 16 children, gives these children chocolate, and measures their level of activity. A researcher obtains a sample mean of M = 102, with a SS = 375.

The researcher finds out that the average activity level among the population is µ = 100, but is unable to find out the population standard deviation.

Does the research have enough evidence to support the hypothesis that sugar causes hyperactivity among children? Use two-tailed test with alpha α=.05

 Fail to reject the null hypothesis and conclude that chocolate does not cause hyperactivity Fail to reject the null hypothesis and conclude that chocolate causes hyperactivity Reject the null hypothesis and conclude that chocolate does not cause hyperactivity Reject the null hypothesis and conclude that chocolate causes hyperactivity

# A researcher is interested in

this is a 2 part question

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

In the last question, you provided the degrees of freedom

A researcher is interested in testing whether college students send more or fewer texts per day, relative to the general population. The researcher finds out that the population average of texts sent per day is µ = 112, but is unable to find out the population standard deviation.

This researcher then recruits 25 college students, and asks about their texting. They report a sample mean of M = 120, with a SS= 1200

What is the effect size (Cohen’s d) for the difference?

# A researcher is interested in

A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 107 students who averaged 32.5 minutes concentrating on their professor during the hour lecture. The standard deviation was 10.3 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean minutes of concentration is between  and   minutes.

c. If many groups of 107 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean minutes of concentration and about  percent will not contain the true population mean minutes of concentration

# A researcher is interested in

A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 148 students who averaged 37.6 minutes concentrating on their professor during the hour lecture. The standard deviation was 12.2 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean minutes of concentration is between  and   minutes.

c. If many groups of 148 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

# A researcher is interested in

A researcher is interested in investigating whether religious affiliation and the brand of sneakers that people wear are associated. The table below shows the results of a survey.

Frequencies of Religions and Sneakers

Protestant 97 87 117
Catholic 68 50 80
Jewish 18 19 38
Other 64 83 70

What can be concluded at the αα = 0.05 significance level?

3. The p-value is Select an answer less than (or equal to) greater than  αα
4. Based on this, we should
• reject the null
• fail to reject the null
• accept the null
5. Thus, the final conclusion is…
• There is sufficient evidence to conclude that sneaker brand and religious affiliation are dependent.
• There is insufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion.
• There is insufficient evidence to conclude that sneaker brand and religious affiliation are dependent.
• There is sufficient evidence to conclude that sneaker brand and religious affiliation are independent.
• There is sufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion.

# A researcher is interested in

A researcher is interested in the effect of the pandemic on social media use among college students. The researcher hypothesizes that college students spend more time on social media than they did before the pandemic.  To test his hypothesis, he randomly selected 50 college students and asked how many hours do they spend on social media per day before and after the pandemic.

1. What is the research question?

Do college students spend more time on social media that they did before the pandemic?

1. What is/are the variable(s)? What graphs can be used to display the variable(s) visually?

1. What statistical test can be used to answer the research question?

# A researcher is interested in

A researcher is interested in the effect of the pandemic on social media use among college students. The researcher hypothesizes that college students spend more time on social media than they did before the pandemic.  To test his hypothesis, he randomly selected 50 college students and asked how many hours do they spend on social media per day before and after the pandemic.

1. What is the research question?

Do college students spend more time on social media that they did before the pandemic?

1. What is/are the variable(s)? What graphs can be used to display the variable(s) visually?

Variables- social media  & college students.

The graph that could be used is

1. What statistical test can be used to answer the research question?

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