# Let x be a random variable tha

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.

 x 0.336 0.296 0.34 0.248 0.367 0.269 y 3.2 7.5 4 8.6 3.1 11.1

(b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.)

 t critical t ±

(d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.)
%

(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.)

 lower limit % upper limit %

(f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.)

 t critical t ±

(g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

 lower limit upper limit

please show steps and work

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 76 64 63 80 63 67 y 51 42 50 47 42 44

Verify that ∑x = 413, ∑y = 276, ∑x2 = 28,699, ∑y2 = 12,774, ∑xy = 19,068, and r = 0.482, and find the P-value for the test that claims ρ is greater zero.

Group of answer choices

0.0005 < P-value < 0.005
0.075 < P-value < 0.10
0.125 < P-value < 0.25
0.10 < P-value < 0.125
P-value > 0.25

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51

(a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.)

(b) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

 t = critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? > 0.
Reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

(c) Find Seab, and x. (Round your answers to four decimal places.)

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)

(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)

 lower limit % upper limit %

(f) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

 t = critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? > 0.
Reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

# Let x be a random variable tha

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient’s doctor are as follows.
 15 17 16 20 14 11 15 18 16 12

(a)
Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x=s=
(b)
Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01.
(i)
What is the level of significance?

# Let x be a random variable tha

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.72. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are as follows.

 4.9 4.2 4.5 4.1 4.4 4.3

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

 x = s =

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.72? Use ? = 0.05.

(a) What is the level of significance?

# Let x be a random variable tha

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean ? = 8050 and estimated standard deviation ? = 2650. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 70 69 81 65 86 y 51 54 45 56 50 49

Given that ∑x = 438, ∑y = 305, ∑x2 = 32,332, ∑y2 = 15,579, ∑xy = 22,302, and r = 0.226, find the P-value for a test claiming that ρ is greater than zero.

 0.25 >  P-value  > 0.10 0.10 >  P-value  > 0.05 0.40 >  P-value  > 0.25 P-value  < 0.0005 P-value  > 0.40X

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 87 88 70 84 78 76 y 53 57 50 51 46 50

Given that Se ≈ 3.054, a ≈ 16.547, b  0.425, and , find the predicted percentage  of successful field goals for a player with x = 73% successful free throws.

 31.0% 5.1% 28.0% 47.6% 14.5%

# Let x be a random variable tha

The Student’s t distribution table gives critical values for the Student’s t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of ? found in the one-tail area row. For a left-tailed test, the column header is the value of ? found in the one-tail area row, but you must change the sign of the critical value t to −t. For a two-tailed test, the column header is the value of ? from the two-tail area row. The critical values are the ±t values shown.

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4†. A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 7.9 with sample standard deviation s = 1.5. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)

 test statistic = critical value = ±

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 63 79 70 80 84 87 y 46 49 45 55 57 58

Find Se. Round your answer to three decimal places.

Group of answer choices

2.522
2.819
2.302
1.994
2.131

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51

Find the predicted percentage  of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)

(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)

 lower limit % upper limit %

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

 t critical t

(g) Find a 90% confidence interval for β. (Round your answers to three decimal places.)

 lower limit upper limit

# Let x be a random variable tha

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

What is the level of significance?
State the null and alternate hypotheses.
H0: μ ≠ 7.4; H1: μ = 7.4
H0: μ = 7.4; H1: μ < 7.4
H0: μ = 7.4; H1: μ ≠ 7.4
H0: μ = 7.4; H1: μ > 7.4
H0: μ > 7.4; H1: μ = 7.4

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.
The Student’s t, since the sample size is large and σ is known.
The Student’s t, since the sample size is large and σ is unknown.
The standard normal, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Estimate the P-value.

P-value > 0.150
0.100 < P-value < 0.150
0.050 < P-value < 0.100
0.020 < P-value < 0.050
P-value < 0.020
Sketch the sampling distribution and show the area corresponding to the P-value.

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.
There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51
(a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.)

 Σx = Σy = Σx2 = Σy2 = Σxy = r =

(b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)

 t = critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0.    Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

(c) Find Seab, and x. (Round your answers to four decimal places.)

 Se = a = b = x =

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)
%

(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)

 lower limit % upper limit %

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

 t = critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0.    Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

# Let X be a random variable tha

Let X be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then X has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the X distribution is about 4.84. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are as follows.

 4.6 4.7 4.7 4.5 4.5 4.1

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

 x = s =

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.84? Use ? = 0.05.

(a) State the null hypotheses

H0

and the alternate hypothesis

H1

.

H0

: μ  —Select— ≥ ≤ > ≠  < =

H1

: μ  —Select— ≠ < = ≥ >  ≤

(b) What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Compute the P-value. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.84.
There is insufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.84.

# Let x be a random variable tha

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient’s doctor are as follows.
 14 19 17 20 15 12 13 18 17 10

(a) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x=
s=
(b) Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01.
(i)
State the null hypotheses

H0

and the alternate hypothesis

H1

.

H0

: μ  —Select— < = ≤ > ≠  ≥

H1

: μ  —Select— > = ≥  ≤ < ≠

(ii) What is the value of the sample test statistic? (Round your answer to three decimal places.)

(iii) Compute the P-value. (Round your answer to four decimal places.)

(iv) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(v) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.
There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.

# Let x be a random variable tha

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.2.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a)
What is the level of significance?

State the null hypothesis

H0

and the alternate hypothesis

H1

.

H0

: μ  —Select— ≤ < > ≠  ≥ =

H1

: μ  —Select— ≥ < >  ≤ = ≠

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since the sample size is large and σ is known.
The standard normal, since the sample size is large and σ is unknown.
The Student’s t, since the sample size is large and σ is known.
The Student’s t, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c)
Calculate the P-value. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.
There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

# Let x be a random variable tha

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) What is the level of significance?

State the null and alternate hypotheses.
H0: μ > 7.4; H1: μ = 7.4
H0: μ = 7.4; H1: μ > 7.4
H0: μ ≠ 7.4; H1: μ = 7.4
H0: μ = 7.4; H1: μ ≠ 7.4
H0: μ = 7.4; H1: μ < 7.4

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.
The Student’s t, since the sample size is large and σ is unknown.
The Student’s t, since the sample size is large and σ is known.
The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.) ___________________?

(c) Estimate the P-value.
P-value > 0.150
0.100 < P-value < 0.150
0.050 < P-value < 0.100
0.020 < P-value < 0.050
P-value < 0.020

Sketch the sampling distribution and show the area corresponding to the P-value.
A plot of the Student’s t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −2.37 and 4 is shaded.

A plot of the Student’s t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.37 and 4 is shaded.

A plot of the Student’s t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.37 is shaded.

A plot of the Student’s t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.37 as well as the area under the curve between 2.37 and 4 are both shaded.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

(a) There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.
(b) There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 44 41 48 51 44 51
(a) Verify that Σx = 438, Σy = 279, Σx2 = 32264, Σy2 = 13059, Σxy = 20493, and r ≈ 0.800.

 Σx =__ Σy =__ Σx2 =__ Σy2 =__ Σxy =__ r =__

(b) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

 t =__ critical t=__

(c) Verify that Se ≈ 2.7729, a ≈ 14.783, b ≈ 0.4345, and x ≈ 73.000.

 Se =__ a =__ b =__ x =__

(d) Find the predicted percentage  of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.)

__ %

(e) Find a 90% confidence interval for y when x = 71. (Round your answers to one decimal place.)

 lower limit __% upper limit __%

(f) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

 t=__ critical t=__

(g) Find a 90% confidence interval for ?. (Round your answers to three decimal places.)

 lower limit =__ upper limit=__

# Let x be a random variable tha

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x for a random sample of 40 does is less than 52 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that

x < 56.8 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6250 and estimated standard deviation σ = 2950. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

What is the probability of x < 3500? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

# Let x be a random variable tha

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

a. What is the value of the sample test statistic? (Round your answer to three decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.

 x 0.338 0.306 0.34 0.248 0.367 0.269 y 3.5 7.7 4 8.6 3.1 11.1

Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901.

Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.)

 t critical t ±

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ differs from 0.
Reject the null hypothesis, there is insufficient evidence that ρ differs from 0.
Fail to reject the null hypothesis, there is insufficient evidence that ρ differs from 0.
Fail to reject the null hypothesis, there is sufficient evidence that ρ differs from 0.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51
(a) Verify that Σx = 438, Σy = 275, Σx2 = 32264, Σy2 = 12727, Σxy = 20231, and r ≈ 0.827.

(g) Find a 90% confidence interval for β. (Round your answers to three decimal places.)

 lower limit upper limit

Interpret its meaning.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. Σx = 438, Σy = 275, Σx2 = 32264, Σy2 = 12727, Σxy = 20231, and r ≈ 0.827.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51

Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)

 t critical t

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.
Reject the null hypothesis, there is insufficient evidence that ρ > 0.
Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.
Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

Se ≈ 3.1191, a ≈ 6.564, b ≈ 0.5379, and x ≈ 73.000.
Find the predicted percentage  of successful field goals for a player with x = 73% successful free throws. (Round your answer to two decimal places.)
%
Find a 90% confidence interval for y when x = 73. (Round your answers to one decimal place.)

 lower limit % upper limit %

Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

 t critical t

Conclusion

Reject the null hypothesis, there is sufficient evidence that β > 0.
Reject the null hypothesis, there is insufficient evidence that β > 0.
Fail to reject the null hypothesis, there is insufficient evidence that β > 0.
Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

Find a 90% confidence interval for β. (Round your answers to three decimal places.)

 lower limit upper limit

Interpret its meaning.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.
For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.

# Let x be a random variable tha

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.5. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

What is the level of significance? ____

What is the value of the sample test statistic? (Round your answer to three decimal places.)____

# Let x be a random variable tha

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6650 and estimated standard deviation σ = 2150. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is approximately normal with μx = 6650 and σx = 2150.
The probability distribution of x is approximately normal with μx = 6650 and σx = 1520.28.
The probability distribution of x is not normal.
The probability distribution of x is approximately normal with μx = 6650 and σx = 1075.00.

What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities increased as n increased.
The probabilities stayed the same as n increased.
The probabilities decreased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.
It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.     It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.
It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

# Let x be a random variable tha

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in a town in Colorado. The x distribution has a mean ? of approximately 75°F and standard deviation ? of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table.

 I II III IV Region underNormal Curve x°F Expected % fromNormal Curve ObservedNumber of Daysin 20 Years μ – 3σ ≤ x < μ – 2σ 51 ≤ x < 59 2.35% 15 μ – 2σ ≤ x < μ – σ 59 ≤ x < 67 13.5% 90 μ – σ ≤ x < μ 67 ≤ x < 75 34% 205 μ ≤ x < μ + σ 75 ≤ x < 83 34% 213 μ + σ ≤ x < μ + 2σ 83 ≤ x < 91 13.5% 86 μ + 2σ ≤ x < μ + 3σ 91 ≤ x < 99 2.35% 11
Use a 1% level of significance

(i) Remember that ? = 75 and ? = 8. Examine the figure above. Write a brief explanation for columns I, II, and III in the context of this problem.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

# Let x be a random variable tha

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 8200 and estimated standard deviation σ = 3000. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 69 and estimated standard deviation ? = 28. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

What is the probability that x < 40? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 54.0 kg and standard deviation ? = 7.8 kg. Suppose a doe that weighs less than 45 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
__ does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 55.2 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x = 55.2 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.
Since the sample average is below the mean, it is quite likely that the doe population is undernourished.
Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.
Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 73 74 80 66 77 77 y 50 52 45 46 52 53

Verify that Se ≈ 3.694, a ≈ 38.254, b  0.153, and , ∑x =447, ∑y =298, ∑x2 =33,419, and ∑y2 =14,858, and use a 5% level of significance to find the P-value for the test that claims that β is greater than zero.

Group of answer choices

Since the P-value is greater than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Since the P-value is equal to α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Since the P-value is less than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Since the P-value is greater than α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Since the P-value is equal to α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

# Let x be a random variable tha

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has a mean μ of approximately 68°F and standard deviation σ of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table.

 I II III IIII Region under Normal Curve x°F Expected % from Normal Curve Observed Number of Days in 20 Years μ – 3σ ≤ x < μ – 2σ 56 ≤ x < 60 2.35% 19 μ – 2σ ≤ x < μ – σ 60 ≤ x < 64 13.5% 78 μ – σ ≤ x < μ 64 ≤ x < 68 34% 202 μ ≤ x < μ + σ 68 ≤ x < 72 34% 220 μ + σ ≤ x < μ + 2σ 72 ≤ x < 76 13.5% 87 μ + 2σ ≤ x < μ + 3σ 76 ≤ x < 80 2.35% 14

(ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with μ = 68 and σ = 4.

(a) What is the level of significance?

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51

(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)

 lower limit % upper limit %

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 67 64 75 86 73 73 y 42 39 48 51 44 51

(c) Find Seab, and x. (Round your answers to four decimal places.)

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)

(f) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

 t = critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? > 0.
Reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is insufficient evidence that ? > 0.
Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 69 66 63 65 76 76 y 54 53 51 43 47 45

Verify that Se ≈ 4.739, a ≈ 67.050, b  –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places.

The 90% confidence interval for β is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47.

The 90% confidence interval for β is from –1.065 to 0.539 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.07 and 0.54.

The 90% confidence interval for β is from –0.882 to 0.355 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.88 and 0.36.

The 90% confidence interval for β is from –1.023 to 0.496 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.02 and 0.50.

The 90% confidence interval for β is from –1.309 to 0.782 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.31 and 0.78.

# Let x be a random variable tha

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

 x 89 64 82 82 72 64 y 61 47 56 47 53 48

Verify that Se ≈ 4.443, a ≈ 22.133, b  0.396, and , ∑x = 453, ∑y = 312, ∑x2 = 34,745, and ∑y2 = 16,388, and find a 98% confidence interval for y when x = 81. Round your final answers to one decimal place.

Group of answer choices

between 35.6 and 72.8
between 35.3 and 73.1
between 35.8 and 72.6
between 37.1 and 71.3
between 35.9 and 72.4

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