Question 1

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 of the two groups is calculated as the average of the two sample variances. This is because equal sample sizes indicate equal representation of each group, and thus equal weight should be given to the variances of each group.

Question 2

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 differences between the means of two independent populations, you can use either a one-tailed or two-tailed test, depending on the research question and hypothesis being tested. A one-tailed test is appropriate when the alternative hypothesis is directional and predicts the direction of the difference between the means. A two-tailed test is appropriate when the alternative hypothesis is non-directional and simply predicts that there is a difference between the means, without specifying the direction.

Question 3

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 dependent samples test) is used when the same group of individuals is tested more than once, under different conditions or at different times. In this case, the same group of 60 students is tested twice - once after two hours of sleep and once after eight hours of sleep. Therefore, a related samples test is appropriate to analyze the data.

Question 4

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

To calculate the degrees of freedom for a pooled-variance t test, we need to use the formula:

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

where n1 and n2 are the sample sizes of the two groups being compared.

In this case, we have two groups (U1B1 and U1B0) with sample sizes of 16 and 25, respectively. So we can calculate the degrees of freedom as:

df = (16-1) + (25-1) = 39

Therefore, the best choice is D: df = 39.

Question 5

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 6

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 instructor would use a t-distribution with 10 degrees of freedom because the degrees of freedom for a paired sample t-test is calculated as n - 1, where n is the number of pairs (in this case, 11 recruits), so 11 - 1 = 10.

Question 7

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

The null hypothesis for testing differences between the means of two related populations is that the population mean difference (μ_D) is equal to zero. Therefore, choice B is the correct option. Choices A, C, and D are incorrect as they do not reflect the correct null hypothesis.

Question 8

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

The answer of In testing for differences between the means...

Question 9

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 10

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 in each independent sample do not need 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, although equal sizes may increase the power of the test.

Question 11

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

Accepted Answer

Repeated measurements from the same individuals are not independent of each other, and therefore can be considered as data collected from two related populations. Such data require different statistical analyses compared to data collected from independent populations.

Question 12

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 in testing for differences between the means of two independent populations is typically that the difference in means is equal to zero. Choice A is the only option that has this in the null hypothesis. The other options suggest alternative hypotheses or have specific values in the null hypothesis, which are not standard for this type of test.

Question 13

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 14

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

Accepted Answer

This statement is true. When testing for differences between the means of two related populations (such as pre- and post-treatment), you can choose either a one-tailed or two-tailed test. A one-tailed test is used when you have a directional hypothesis (i.e. you expect one population to have a higher or lower mean than the other), while a two-tailed test is used when you have a non-directional hypothesis (i.e. you don't have a specific expectation about which population will have a higher or lower mean).

Question 15

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 lecturer took a random sample of size 10 from each group, this is a situation for independent samples, not related samples. Therefore, the lecturer should use a t test with independent samples, not related samples.

Question 16

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 is calculated as (n1 - 1) + (n2 - 1), where n1 and n2 are the sample sizes of the two populations. Therefore, the degrees of freedom for this test would be (20-1) + (20-1) = 38. The correct answer is C.

Question 17

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 involves the variable of interest being the difference between the values of the observations within the same individual or entity, rather than between separate individuals or entities. Examples of related populations include before and after measurements on the same sample or matched pairs. The other options listed involve the variable of interest being the means or variances of separate populations, not the differences within related populations.

Question 18

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

When variances are equal and sample sizes are small, a t test with independent samples is appropriate.

Question 19

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

The t-distribution should be used for small sample sizes (n<30) where the population standard deviation is unknown. With 11 recruits, a t-distribution with 10 degrees of freedom would be appropriate for testing whether there was a significant improvement in completion time before and after basic training.

Question 20

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 that population sizes are equal or that sample variances are equal. Therefore, the best choice is B.

Quiz 10: Hypothesis Testing: Two Sample Tests

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

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

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.

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

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 11 degrees of freedom.

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

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

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

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.

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,the null hypothesis is

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

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

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

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

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.

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

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 presuming equal variances 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 with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to