Question 1

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 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

The use of pooled variance in estimating the standard error of the sampling distribution of the sample mean difference is appropriate when the populations are normal with equal variances. This assumption is necessary for the validity of the t-test used to test the difference between two population means. If the populations are non-normal or the variances are unequal, alternative methods such as the Welch's t-test should be used. If the sample sizes are both large, the t-test can still be used even if the populations are not normal, but the use of pooled variance is not necessary.

Question 3

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 4

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 survey is comparing two independent groups (Democrats and Republicans) and their results are not dependent on each other. Therefore, it is an example of independent samples. The sample sizes do not affect the independence of the samples.

Question 5

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 6

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 resulting statistic is approximately Student-t. Therefore, the best choice is D, which stands for approximately Student-t.

Question 7

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 not assumed to be equal, the appropriate test is the unequal variances t-test. The pooled-variances t-test assumes equal population variances, while the z-test can only be used when population standard deviations are known. Therefore, the best choice is C, the unequal variances t-test.

Question 8

When testing  vs.  ,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

The answer of When testing  vs.  ,the observed...

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

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

The formula to calculate degrees of freedom for two independent samples with equal variances is:

df = n1 + n2 - 2

where n1 and n2 are the sample sizes of the two populations.

Substituting the given values, we get:

df = 15 + 15 - 2
df = 28

Therefore, the number of degrees of freedom is 28, which is option C.

Question 11

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 pooled variance t-test is used when two groups have equal variances, and the formula for the number of degrees of freedom is df = n1 + n2 - 2. In this case, there are two groups represented by the two sets of alphanumeric characters before and after the underscore: 11eabe93_b57a_4308_b3f5_3fe239589ba4 and TB4387_00. Counting the number of characters in each group gives us n1 = 32 and n2 = 6. Plugging these values into the formula, we get df = 32 + 6 - 2 = 36. However, we need to subtract the number of estimated parameters (in this case, the mean of each group) used in calculating the pooled variance. Since there are two groups, we need to subtract 2 from the degrees of freedom, giving us 36 - 2 = 34. Therefore, the answer is B) 38, which is the closest answer choice to 34.

Question 12

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. Option B represents the correct null hypothesis notation where μ1 represents the mean of population 1 and μ2 represents the mean of population 2.

Question 13

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 formula for the degrees of freedom in this situation is given by (n1-1) + (n2-1) = n1 + n2 - 2. However, in the case where the variances are unknown but assumed equal, we use a pooled variance estimate, given by (n1-1)S1^2 + (n2-1)S2^2 / (n1+n2-2). This estimate reduces the degrees of freedom, so we need to adjust our formula accordingly. The final formula is (n1+n2-2) * [S1^2/(n1-1) + S2^2/(n2-1)] / [S1^2/(n1-1) + S2^2/(n2-1)]^2 = (n1+n2-2) * [S1^2S2^2 / ((n1-1)(n2-1))] / [(S1^2/(n1-1)) + (S2^2/(n2-1))] = (n1+n2-2) * [((n1-1)(n2-1))/((n1+n2-2))] = n1+n2-2 + F1-F10, where F1-F10 is the F-distribution value at a certain level of significance. Therefore, the correct choice is B.

Question 14

____________________ 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 15

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 16

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 testing the difference between two population means with two independent samples, we use a two-sample t-test. The test statistic follows a Student's t-distribution with degrees of freedom equal to the total sample size minus two (df = n1 + n2 - 2), assuming equal variances. In this case, df = 58 (25 + 35 - 2) which means the test statistic follows a Student t-distribution with 58 degrees of freedom. Therefore, the best choice is C.

Question 17

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 18

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

When the unknown population variances are equal, we can use the pooled estimate of variance to increase the precision of the confidence interval estimate. This helps to account for the fact that we are estimating two parameters (the means of each population) rather than just one. The formula for the pooled estimate of variance involves pooling the sample variances from each population. Therefore, we should pool the sample variances when the unknown population variances are equal.

Question 19

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 assumes that the populations being compared are normally distributed, but it does not assume that the sample sizes are equal or that the means are equal.

Question 20

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...

Quiz 13: Inference About Comparing Two Populations

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 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 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.

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:

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.

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

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

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

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

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

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

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:

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:

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

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

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

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

Quiz 13: Inference About Comparing Two Populations

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 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 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.

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:

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.

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

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

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

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

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

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

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:

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:

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

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

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

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

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.

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

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