Question 1

When testing  the observed value of the z-score was found to be −2.15.Then,the p-value for this test would be
A).0158
B).0316
C).9842
D).9684

Accepted Answer

To calculate the p-value, we need to find the area under the normal distribution curve to the left of the z-score of -2.15. Using a standard normal distribution table or calculator, we find that this area is 0.0316 (or approximately 0.032). Therefore, the p-value for this test is 0.0316 which is the option B.

Question 2

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference  if:
A)the sample sizes are both large.
B)the populations are normal with equal variances.
C)the populations are non-normal with unequal variances.
D)All of these choices are true.

Accepted Answer

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference when the populations are normal with equal variances. The pooled variance combines the variances from both samples into one estimate, assuming that the population variances are equal. This results in a more accurate estimate of the standard error of the sampling distribution and improves the power of the hypothesis test. If the sample sizes are both large, a normal approximation can be used even if the populations are not normal or have unequal variances. However, in this case, the pooled variance may not be the best estimate of the true variance, and other methods may be more appropriate. Therefore, choice B is the best choice.

Question 3

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means  .Assume the population variances are known.The sampling distribution of the sample mean difference  is:
A)normally distributed.
B)approximately normal.
C)Student t-distributed with 88 degrees of freedom.
D)None of these choices.

Accepted Answer

The answer of Two independent samples of sizes 40 and...

Question 4

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom is: A)n₁ + n₂ B)n₁ + n₂ − 2 C)n₁ + n₂ − 1 D)None of these choices

Accepted Answer

The degrees of freedom for the t-test when testing differences between the means of two independent populations, assuming equal but unknown variances, is calculated as the sum of the sample sizes of both groups minus 2. This is represented by $n_1 + n_2 - 2$, which matches choice B.

Question 5

The equal-variances test statistic of is Student t-distributed with n₁ + n₂ − 2 degrees of freedom provided that the two populations are ____________________.

Accepted Answer

The answer of The equal-variances test statistic of  is...

Question 6

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of:
A)independent samples.
B)dependent samples.
C)independent samples only if the sample sizes are equal.
D)dependent samples only if the sample sizes are equal.

Accepted Answer

The samples of registered Democrats and Republicans are independent because the participants in one sample do not affect or influence the participants in the other sample. The sample sizes being equal or not does not affect the independence of the samples. Therefore, this is an example of independent samples.

Question 7

Given the information:  ,the number of degrees of freedom that should be used in the pooled variance t-test is:
A)40
B)38
C)15
D)25

Accepted Answer

The answer of Given the information:  ,the number of...

Question 8

If we are testing for the difference between the means of two independent populations with equal variances,samples of n₁ = 15 and n₂ = 15 are taken,then the number of degrees of freedom is equal to A)13 B)14 C)28 D)29

Accepted Answer

When testing for the difference between the means of two independent populations with equal variances and samples of size n1 and n2, the number of degrees of freedom is given by df = n1 + n2 - 2. Plugging in the given values, we get df = 15 + 15 - 2 = 28. Therefore, the correct answer is choice C.

Question 9

When the sample sizes are equal,the pooled variance of the two samples is the ____________________ of the two sample variances.

Accepted Answer

The answer of When the sample sizes are equal,the pooled...

Question 10

Suppose we randomly selected 250 people,and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:
A)observational.
B)experimental.
C)matched.
D)None of these choices.

Accepted Answer

The data are observational because the assignment to groups is based on survey responses rather than manipulation or intervention by the researcher.

Question 11

The t-test for the difference between the means of two independent populations assumes that the respective:
A)sample sizes are equal.
B)populations are normal.
C)means are equal.
D)All of these choices are true.

Accepted Answer

The t-test for the difference between the means of two independent populations assumes that the populations being compared are normal. The assumption of equal sample sizes is not necessary for the t-test, but it can affect the power of the test. The assumption of equal means is what the t-test aims to test.

Question 12

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

Accepted Answer

The answer of ____________________ samples are those for which the...

Question 13

The unequal-variances test statistic of  has an approximate ____________________ distribution with  degrees of freedom.

Accepted Answer

The answer of The unequal-variances test statistic of  has...

Question 14

In testing for differences between the means of two independent populations the null hypothesis is:
A) 
B) 
C) 
D)

Accepted Answer

The null hypothesis in testing for differences between the means of two independent populations is that there is no significant difference between the means of the two populations. Option B is the only one that presents a complete null hypothesis statement.

Question 15

Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown).In order to test the difference between the population means,the test statistic is:
A)a standard normal random variable.
B)approximately standard normal random variable.
C)Student t-distributed with 58 degrees of freedom.
D)Student t-distributed with 33 degrees of freedom.

Accepted Answer

When the population variances are unknown, we use the t-distribution to test the difference between population means. Since the sample sizes are different, we use the pooled variance and the degrees of freedom are (n1-1) + (n2-1) = 58. Therefore, the correct choice is C, Student t-distributed with 58 degrees of freedom.

Question 16

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal,two independent samples are drawn from the populations.Which of the following tests is appropriate?
A)z-test
B)pooled-variances t-test
C)unequal variances t-test
D)None of these choices.

Accepted Answer

When population variances are unknown and assumed to be unequal, the appropriate test to use is the unequal variances t-test. This test takes into account the possibility of the two populations having different variances, which can affect the calculation of the standard error and therefore the test statistic. The z-test is only appropriate when the population variances are known, while the pooled-variances t-test assumes that the population variances are equal. Thus, the correct choice is the unequal variances t-test (option C).

Question 17

When two population variances are ____________________ we estimate each population variance with its sample variance.The test statistic of is approximately Student t-distributed with n₁ + n₂ − 2 degrees of freedom.

Accepted Answer

The answer of When two population variances are ____________________ we...

Question 18

A political analyst in Iowa surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of ____________________ samples.

Accepted Answer

The answer of A political analyst in Iowa surveys a...

Question 19

In testing the difference between the means of two normal populations using two independent samples when the population variances are unequal,the sampling distribution of the resulting statistic is:
A)normal.
B)Student-t.
C)approximately normal.
D)approximately Student-t.

Accepted Answer

When the population variances are unequal and the sample sizes are small, the sampling distribution of the statistic is approximately Student-t. Therefore, the best choice is D, which corresponds to approximately Student-t.

Question 20

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations,we:
A)pool the sample variances when the unknown population variances are equal.
B)pool the sample variances when the population variances are known and equal.
C)pool the sample variances when the population means are equal.
D)never pool the sample variances.

Accepted Answer

We pool the sample variances when the unknown population variances are equal, using the pooled variance formula to increase precision and accuracy in constructing the confidence interval estimate for the difference between the means of two independent normally distributed populations. When the population variances are not equal, we use the separate variances formula, which does not involve pooling. When the population variances are known and equal, we also use the pooled variance formula. Pooling is not necessary when the population means are equal or different, as it only affects the estimation of the variance of the difference between the sample means.

Quiz 13: Inference About Comparing Two Populations

When testing the observed value of the z-score was found to be −2.15.Then,the p-value for this test would be

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means .Assume the population variances are known.The sampling distribution of the sample mean difference is:

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom is:

The equal-variances test statistic of is Student t-distributed with n₁ + n₂ − 2 degrees of freedom provided that the two populations are ____________________.

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of:

Given the information: ,the number of degrees of freedom that should be used in the pooled variance t-test is:

If we are testing for the difference between the means of two independent populations with equal variances,samples of n₁ = 15 and n₂ = 15 are taken,then the number of degrees of freedom is equal to

When the sample sizes are equal,the pooled variance of the two samples is the ____________________ of the two sample variances.

Suppose we randomly selected 250 people,and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:

The t-test for the difference between the means of two independent populations assumes that the respective:

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

The unequal-variances test statistic of has an approximate ____________________ distribution with degrees of freedom.

In testing for differences between the means of two independent populations the null hypothesis is:

Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown) .In order to test the difference between the population means,the test statistic is:

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal,two independent samples are drawn from the populations.Which of the following tests is appropriate?

When two population variances are ____________________ we estimate each population variance with its sample variance.The test statistic of is approximately Student t-distributed with n₁ + n₂ − 2 degrees of freedom.

A political analyst in Iowa surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of ____________________ samples.

In testing the difference between the means of two normal populations using two independent samples when the population variances are unequal,the sampling distribution of the resulting statistic is:

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations,we:

Quiz 13: Inference About Comparing Two Populations

When testing the observed value of the z-score was found to be −2.15.Then,the p-value for this test would be

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means .Assume the population variances are known.The sampling distribution of the sample mean difference is:

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom is:

The equal-variances test statistic of is Student t-distributed with n1 + n2 − 2 degrees of freedom provided that the two populations are ____________________.

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of:

Given the information: ,the number of degrees of freedom that should be used in the pooled variance t-test is:

If we are testing for the difference between the means of two independent populations with equal variances,samples of n1 = 15 and n2 = 15 are taken,then the number of degrees of freedom is equal to

When the sample sizes are equal,the pooled variance of the two samples is the ____________________ of the two sample variances.

Suppose we randomly selected 250 people,and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:

The t-test for the difference between the means of two independent populations assumes that the respective:

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

The unequal-variances test statistic of has an approximate ____________________ distribution with degrees of freedom.

In testing for differences between the means of two independent populations the null hypothesis is:

Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown) .In order to test the difference between the population means,the test statistic is:

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal,two independent samples are drawn from the populations.Which of the following tests is appropriate?

When two population variances are ____________________ we estimate each population variance with its sample variance.The test statistic of is approximately Student t-distributed with n1 + n2 − 2 degrees of freedom.

A political analyst in Iowa surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of ____________________ samples.

In testing the difference between the means of two normal populations using two independent samples when the population variances are unequal,the sampling distribution of the resulting statistic is:

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations,we:

The equal-variances test statistic of is Student t-distributed with n₁ + n₂ − 2 degrees of freedom provided that the two populations are ____________________.

If we are testing for the difference between the means of two independent populations with equal variances,samples of n₁ = 15 and n₂ = 15 are taken,then the number of degrees of freedom is equal to

When two population variances are ____________________ we estimate each population variance with its sample variance.The test statistic of is approximately Student t-distributed with n₁ + n₂ − 2 degrees of freedom.