Question 1

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females,then the test is one-tailed.

Accepted Answer

The null hypothesis does not specify a direction, so the test would be two-tailed.

Question 2

When dependent samples are used to test for differences in the means,we pool the sample variances.

Accepted Answer

When testing for differences in means with dependent samples, we typically analyze the differences between pairs, not the variance across all samples, so there's no pooling of variances as is done in independent samples t-tests.

Question 3

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here.  At the 0.01 significance level,we ask if there is a difference in the mean number of times men and women send a Twitter message in a day. What is the value of the test statistic for this hypothesis test?

Accepted Answer

D

Question 4

If two dependent samples of size 20 are used to test the difference between the means,the degrees of freedom for a t-statistic are 19.

Accepted Answer

The degrees of freedom for a dependent t-test are equal to the sample size minus 1. Therefore, if the sample size is 20, the degrees of freedom would be 19.

Question 5

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal.  At the 0.01 significance level,what is the conclusion about the way women and men save?

Accepted Answer

The answer of A recent study focused on the amount...

Question 6

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City,then the test is two-tailed.

Accepted Answer

A two-tailed test is appropriate when the null hypothesis states that there is no difference between the two groups being compared. In this case, the null hypothesis is that there is no difference between the mean net income of retail stores in Chicago and New York City, which means that a two-tailed test is appropriate.

Question 7

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the sample standard deviations are pooled to compute the best estimated variance.

Accepted Answer

This statement is true. When the two population standard deviations are assumed to be equal but unknown, the sample standard deviations are pooled to compute the best estimated variance, which is used in calculating the t statistic for hypothesis testing. This approach is known as the pooled variance method.

Question 8

If we are testing for the difference between two population means,it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Accepted Answer

For a two-sample mean test, independence of observations is assumed between the two groups being compared. This is necessary for the assumptions of the test to be met and for the results to be valid.

Question 9

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here.  At the 0.01 significance level,we ask if there is a difference in the mean number of times men and women send a Twitter message in a day. What is the p-value for this hypothesis test?

Accepted Answer

Since the p-value is less than the significance level of 0.01, we can reject the null hypothesis and conclude that there is a significant difference in the mean number of times men and women send a Twitter message in a day. The correct p-value for this test is 0.0164. Therefore, the best choice is B.

Question 10

If the null hypothesis that two means are equal is true,where will 97% of the computed z-values lie between?

Accepted Answer

The answer of If the null hypothesis that two means...

Question 11

Assuming the population variances are known,the population variance of the difference between two means is ________.

Accepted Answer

The formula to calculate the variance of the difference between two means is Variance of Difference = Variance of Sample 1 / Sample Size 1 + Variance of Sample 2 / Sample Size 2. Since the population variances are known, we can use the population variances instead of the sample variances. Therefore, the population variance of the difference between two means is the sum of the two population variances.

Question 12

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)− 1.

Accepted Answer

The formula provided is incorrect and not the standard way to calculate degrees of freedom when testing for the difference between two population means with equal and unknown standard deviations. The correct approach typically involves using the sample sizes of the two groups and a formula related to the pooled variance estimate, often simplified in the form of the Welch-Satterthwaite equation for unequal variances or directly calculated for equal variances.

Question 13

A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.

Accepted Answer

In a paired sample, the same group of subjects is measured twice under two different conditions. In this scenario, the grades from two different classes are not measured on the same group of subjects, so it is not a paired sample. Instead, this would be an example of an independent samples t-test.

Question 14

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal.  At the 0.01 significance level,do women save more money than men? What is the critical value for this hypothesis test?

Accepted Answer

The answer of A recent study focused on the amount...

Question 15

When dependent samples are used to test for differences in the means,we compute paired differences.

Accepted Answer

This statement is true. When using dependent samples, we compare the means of the paired differences, which involves computing the differences between each pair of observations and then calculating the mean of these differences.

Question 16

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal.  At the 0.01 significance level,do women save more money than men? What is the value of the test statistic for this hypothesis test?

Accepted Answer

The answer of A recent study focused on the amount...

Question 17

A recent study focused on the number of times men and women send a Twitter message in a day. The sample information is summarized here.  At the 0.01 significance level,we ask if there is a difference in the mean number of times men and women send a Twitter message in a day. What is the test statistic for this hypothesis?

Accepted Answer

The answer of A recent study focused on the number...

Question 18

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here.  At the 0.01 significance level,is there a difference in the mean number of times men and women send a Twitter message in a day? Based on the p-value,what is your conclusion?

Accepted Answer

The answer of A recent study focused on the number...

Question 19

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal.  At the 0.01 significance level,do women save more money than men? What is the test statistic for this hypothesis?

Accepted Answer

The answer of A recent study focused on the amount...

Question 20

When the standard deviations are equal but unknown,a test for the differences between two population means has n − 1 degrees of freedom.

Accepted Answer

When comparing two population means with equal but unknown standard deviations, the degrees of freedom for the test are calculated using a formula that combines the sample sizes of both groups, not simply n - 1. The formula for degrees of freedom in this case is more complex, often involving both sample sizes.

Quiz 11: Two-Sample Tests of Hypothesis

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females,then the test is one-tailed.

When dependent samples are used to test for differences in the means,we pool the sample variances.

If two dependent samples of size 20 are used to test the difference between the means,the degrees of freedom for a t-statistic are 19.

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,what is the conclusion about the way women and men save?

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City,then the test is two-tailed.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the sample standard deviations are pooled to compute the best estimated variance.

If we are testing for the difference between two population means,it is assumed that the sample observations from one population are independent of the sample observations from the other population.

If the null hypothesis that two means are equal is true,where will 97% of the computed z-values lie between?

Assuming the population variances are known,the population variance of the difference between two means is ________.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n1)(n2)− 1.

A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,do women save more money than men? What is the critical value for this hypothesis test?

When dependent samples are used to test for differences in the means,we compute paired differences.

A recent study focused on the amount of money single men and women save monthly. The information is summarized here. Assume that the population standard deviations are equal. At the 0.01 significance level,do women save more money than men? What is the test statistic for this hypothesis?

When the standard deviations are equal but unknown,a test for the differences between two population means has n − 1 degrees of freedom.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)− 1.