A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum

Mean 75.31914894 65.65957447

Variance 118.613321 801.1424607

Observations 47 47

Pooled Variance 459.8778908

Hypothesized Mean Difference 0

df 92

t Stat 2.1835887807

P(T<=)one tail 0.015768226

t Critical one-tail 1.661585397

P(T<=t) two-tail 0.031536452

t Critical two-tail 1.986086317

You decide to use the conventional p=.05 as your cutoff for statistical significance. What do you conclude from this analysis?

a. The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b. We cannot be sufficiently confident that there is a relationship between the math curriculum followed and students’ test scores.

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum

Mean 65.06382979 66.5106383

Variance 822.4523589 127.5161887

Obervations 47 47

Hypothesized Mean Difference 0

df 60

t Stat -0.321814324

P(T<=t) 0.37

t Critical one-tail 1.670648865

P(T<=t) two-tail 0.75

t Critical two-tail 2.000297822

You decide to use the conventional p=.05 as your cutoff for statistical significance. What do you conclude from this analysis?

a. The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b. We should reject the null hypothesis, which is that the two groups’ means are equal in the populaton of 5th graders.

c. We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d. We should reject the null hypothesis, which is that the two groups’means are not equal in the population of 5th graders.

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum

Mean 75.31914894 75.4893617

Variance 118.613321 33.8640148

Obervations 47 47

Hypothesized Mean Difference 0

df 70

t Stat -0.094501437

P(T<=t) 0.46

t Critical one-tail 1.666914479

P(T<=t) two-tail 0.92

t Critical two-tail 1.994437112

You decide to use the conventional p=.05 as your cutoff for statistical significance. What do you conclude from this analysis?

a. The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b. We should reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

c. We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d. We should reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

e. We should not reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

Mean 68.76595745 75.4893617

Variance 22.226642 33.8640148

Obervations 47 47

Hypothesized Mean Difference 0

df 88

t Stat -6.154501628

P(T<=t) 0.00

t Critical one-tail 1.662354029

P(T<=t) two-tail 0.00

t Critical two-tail 1.987289865

a. The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b. We should reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

c. We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d. We should reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

e. We should not reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: t-test: Two-Sample Assuming Equal Variances

Old Curriculum New Curriculum

Mean 75.31914894 65.65957447

Variance 118.613321 801.1424607

Obervations 47 47

Hypothesized Mean Difference 0

df 92

t Stat 2.183587807

P(T<=t) one-tail 0.015768226

t Critical one-tail 1.661585397

P(T<=t) two-tail 0.031536452

t Critical two-tail 1.986086317

- The wrong t-test was conducted because of the relative sizes of the two groups’ variances.
- We cannot be sufficiently confident that there is a relationship between the math curriculum followed and students’ test scores.
- There probably is a relationship between the math curriculum followed and students’ test scores.

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