Question 1

The t test for the mean difference between two related populations assumes that the
A) population sizes are equal.
B) population of differences is approximately normal or sample sizes are large enough.
C) sample variances are equal.
D) All of the above.

Accepted Answer

The t test for the mean difference between two related populations assumes that the population of differences is approximately normal or sample sizes are large enough. It does not assume equal population sizes or equal sample variances. Therefore, option B is the best choice.

Question 2

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?
A) A test for the difference between the means of two independent populations.
B) A test for the equality of variances from two independent populations.
C) A test for the difference between the means of two related populations.
D) All of the above.

Accepted Answer

A test for the difference between the means of two related populations, also known as a paired t-test, compares the difference between paired observations in two groups, rather than the observations themselves. The other options listed involve comparing the means or variances of two independent populations, making the variable of interest the actual observations, not just the difference between them.

Question 3

When the sample sizes are equal,the pooled variance of the two groups is the average of the two sample variances.

Accepted Answer

When the sample sizes are equal, the pooled variance is calculated as the weighted average of the two sample variances, where the weights are equal. Therefore, the pooled variance is the average of the two sample variances.

Question 4

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom

Accepted Answer

The correct degrees of freedom for a paired t-test (which is appropriate for this scenario) would be 10, not 11, because degrees of freedom are calculated as n - 1, where n is the number of pairs (11 pairs in this case).

Question 5

In testing for differences between the means of two independent populations,the null hypothesis is A) H₀: μ₁ - μ₂ = 0. B) H₀: μ₁ - μ₂ < 2. C) H₀: μ₁ - μ₂ > 0. D) H₀: μ₁ - μ₂ = 2.

Accepted Answer

The null hypothesis for testing differences between the means of two independent populations is typically that the difference between the population means is equal to zero. The null hypothesis is usually denoted as H0: μ1 - μ2 = 0, where μ1 and μ2 are the population means of the two populations being compared. Choice A is the closest option to this typical null hypothesis, as it has the same format with the specific populations denoted as ₁ and ₂.

Question 6

If you are testing for the difference between the means of two independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to A) 39. B) 19. C) 18. D) 38.

Accepted Answer

The answer of If you are testing for the difference...

Question 7

When you test for differences between the means of two independent populations,you can only use a two-tailed test.

Accepted Answer

When testing for the difference between two independent population means, you can use a two-tailed test or a one-tailed test, depending on the research question and hypothesis being tested.

Question 8

In testing for differences between the means of two related populations where the variance of the differences is unknown,the degrees of freedom are A) n₁ + n₂ - 1. B) n - 1. C) n₁ + n₂ - 2. D) n - 2.

Accepted Answer

The degrees of freedom for testing differences between the means of two related populations, where the variance is unknown, is n - 1, where n is the number of paired differences.

Question 9

The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

Accepted Answer

The sample sizes do not have to be the same to test for differences between the means of two independent populations. Statistical tests, such as the independent samples t-test, can accommodate different sample sizes.

Question 10

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

Accepted Answer

Yes, it is possible to use either a one-tailed or two-tailed test when testing for differences between the means of two related populations. The choice of test will depend on the research question and the directional hypothesis being tested. A one-tailed test is appropriate when there is a specific directional hypothesis or when the research question is focused on one particular direction, while a two-tailed test is used when there is no specific directional hypothesis or when both directions are of equal interest.

Question 11

In testing for differences between the means of two related populations,the null hypothesis is A) H₀: μ_D < 0. B) H₀: μ_D = 0. C) H₀: μ_D = 2. D) H₀: μ_D > 0.

Accepted Answer

In testing for differences between the means of two related populations, the null hypothesis is that the mean difference (µ1 - µ2) is equal to zero. Therefore, the correct null hypothesis is H₀: μ_D = 0.

Question 12

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 approximately normal.
C) sample variances are equal.
D) All of the above.

Accepted Answer

The t test for the difference between the means of two independent populations assumes that the populations are approximately normal. While equal sample sizes and equal sample variances are preferred, they are not absolutely necessary. Therefore, the best choice is option B, which states that the assumption of normality is necessary for the t test for the difference between two means of independent populations.

Question 13

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with independent samples.

Accepted Answer

Since the sample sizes are equal and the variances are equal, the appropriate test to use is a t test with independent samples.

Question 14

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 10 degrees of freedom.

Accepted Answer

Since the sample size is only 11, it is appropriate to use a t-distribution to test for improvement. The degrees of freedom is equal to the sample size minus one, so in this case it is 10.

Question 15

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each two tests: one given after two hours of sleep and one after eight hours of sleep.The test the researcher should use would be a related samples test.

Accepted Answer

A related samples test (also known as a paired samples test or a dependent samples test) would be appropriate in this scenario because each of the 60 students is taking two tests (before and after different amounts of sleep) and the results are being compared within each individual student. This is in contrast to an independent samples test, which would be appropriate if two different groups of students (for example, one group who had two hours of sleep and another group who had eight hours of sleep) were being compared to each other.

Question 16

Repeated measurements from the same individuals are an example of data collected from two related populations.

Accepted Answer

Repeated measurements from the same individuals represent data collected from the same population over time, which is related. Therefore, it represents data collected from two related populations.

Question 17

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are A) n₁ + n₂ - 2. B) n₁ + n₂ - 1. C) n - 2. D) n - 1.

Accepted Answer

When testing for differences between the means of two independent populations with unknown but equal variances, the degrees of freedom are calculated as n₁ + n₂ - 2, where n₁ and n₂ are the sample sizes of the two populations.

Question 18

Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. S₁² = 4 S₂² = 6 N₁ = 16 n₂ = 25 A) df = 16 B) df = 41 C) df = 25 D) df = 39

Accepted Answer

The formula for degrees of freedom in a pooled-variance t-test is df = (n1-1) + (n2-1), where n1 and n2 are the sample sizes. Using the formula for each group, we get df1 = 15 and df2 = 24. Therefore, the total degrees of freedom is df1 + df2 = 39. Therefore, the correct choice is D.

Question 19

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with related samples.

Accepted Answer

Since the sample sizes for upper and lower students are independent, a t test with independent samples should be used. It is also stated in the problem that the variances are equal, which further supports the use of a t test with independent samples.

Question 20

If you are testing for the difference between the means of two independent populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to A) 19. B) 39. C) 38. D) 18.

Accepted Answer

The number of degrees of freedom for a two-sample t-test is calculated using the formula:

df = (n1-1) + (n2-1)

where n1 and n2 are the sample sizes for the two populations being compared.

Substituting the given values, we get:

df = (20-1) + (20-1) = 38

Therefore, the correct answer is C) 38.

Quiz 10: Hypothesis Testing: Two-Sample Tests

The t test for the mean difference between two related populations assumes that the

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

When the sample sizes are equal,the pooled variance of the two groups is the average of the two sample variances.

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom

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

If you are testing for the difference between the means of two independent populations presuming equal variances with samples of n1 = 20 and n2 = 20,the number of degrees of freedom is equal to

When you test for differences between the means of two independent populations,you can only use a two-tailed test.

In testing for differences between the means of two related populations where the variance of the differences is unknown,the degrees of freedom are

The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

In testing for differences between the means of two related populations,the null hypothesis is

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

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 10 degrees of freedom.

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each two tests: one given after two hours of sleep and one after eight hours of sleep.The test the researcher should use would be a related samples test.

Repeated measurements from the same individuals are an example of data collected from two related populations.

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

Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. S12 = 4 S22 = 6 N1 = 16 n2 = 25

If you are testing for the difference between the means of two independent populations with samples of n1 = 20 and n2 = 20,the number of degrees of freedom is equal to

If you are testing for the difference between the means of two independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to

Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. S₁² = 4 S₂² = 6 N₁ = 16 n₂ = 25

If you are testing for the difference between the means of two independent populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to