Question 1

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:
A) normal distribution.
B) binomial distribution.
C) Student t-distribution.
D) F-distribution.

Accepted Answer

The Student t-distribution is used for hypothesis testing of population means when the sample size is small and/or the population standard deviation is unknown. Since the data is gathered from a matched pairs experiment, we are comparing the means of two dependent samples, and the paired differences are used to calculate the test statistic. If the paired differences are normally distributed, then the t-distribution can be used to make inferences about the population means. The normal distribution is used for hypothesis testing when the sample size is large and the population standard deviation is known. The binomial distribution is used for counting the number of successful outcomes in a fixed number of independent trials, and the F-distribution is used for hypothesis testing of the equality of two population variances.

Question 2

The symbol  refers to:
A) the difference in the means of two independent populations.
B) one matched pairs difference.
C) the mean difference in the pairs of observations.
D) None of these choices.

Accepted Answer

The answer of The symbol  refers to:
A) the difference...

Question 3

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...

Question 4

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 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

The pooled variance estimator is the ____________________ average of the two sample variances.

Accepted Answer

The answer of The pooled variance estimator is the ____________________...

Question 7

When the population variances are unknown and unequal, we estimate each population variance with its ____________________ variance.

Accepted Answer

The answer of When the population variances are unknown and...

Question 8

The test for the mean difference in a matched pairs design requires the differences to have a(n) ____________________ distribution.

Accepted Answer

The answer of The test for the mean difference in...

Question 9

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 10

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as:
A) matched pairs.
B) independent samples.
C) nonrandom samples.
D) None of these choices.

Accepted Answer

Matched pairs is the term used when each pair of observations are related to each other in some way, allowing for a logical comparison between the two. This often occurs in experiments where the same individual or object is measured twice under different conditions.

Question 11

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 political analyst is comparing two groups (Democrats and Republicans) that are unrelated to each other, therefore the samples are independent. The sample sizes do not affect the independence of the samples.

Question 12

The unequal-variances test statistic of has an approximate ____________________ distribution with n₁ + n₂- 2 degrees of freedom.

Accepted Answer

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

Question 13

If you are testing to see if a weight loss program is working, and you subtract the weights before - after for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

Accepted Answer

The answer of If you are testing to see if...

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

Two measurements from the same individuals is an example of data collected from a(n) ____________________ experiment.

Accepted Answer

The answer of Two measurements from the same individuals is...

Question 16

In a matched pairs experiment the parameter of interest is the ____________________ of the population of ____________________.

Accepted Answer

The answer of In a matched pairs experiment the parameter...

Question 17

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:
A) 10
B) 20
C) 9
D) 18

Accepted Answer

In a matched pairs experiment, each pair contributes one degree of freedom, which means there are 10 pairs or 10 degrees of freedom in total. However, because the paired samples are dependent, one degree of freedom is lost, resulting in 9 degrees of freedom for the t-test. Therefore, the best choice is C.

Question 18

The pooled-variances t-test is used when the two population variances are ____________________.

Accepted Answer

The answer of The pooled-variances t-test is used when the...

Question 19

The degrees of freedom for a test of the mean of the paired differences is the number of ____________________ minus ____________________.

Accepted Answer

The answer of The degrees of freedom for a test...

Question 20

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

This is an observational study as the researchers are observing and recording data without manipulating any variables. They are simply assigning people to groups based on their survey responses and then recording their blood pressure. If it were an experimental study, the researchers would have manipulated a variable (e.g. giving one group a medication) and then compared the blood pressure of the two groups. Matched studies typically involve pairing subjects who are similar in some way (e.g. age, gender) and then comparing outcomes between the two groups. However, there is no indication that this study was matched.

Quiz 12: Inference About Comparing Two Populations, Part 1

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:

The symbol refers to:

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

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.

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.

The pooled variance estimator is the ____________________ average of the two sample variances.

When the population variances are unknown and unequal, we estimate each population variance with its ____________________ variance.

The test for the mean difference in a matched pairs design requires the differences to have a(n) ____________________ distribution.

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:

The unequal-variances test statistic of has an approximate ____________________ distribution with n₁ + n₂- 2 degrees of freedom.

If you are testing to see if a weight loss program is working, and you subtract the weights before - after for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

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

Two measurements from the same individuals is an example of data collected from a(n) ____________________ experiment.

In a matched pairs experiment the parameter of interest is the of the population of .

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:

The pooled-variances t-test is used when the two population variances are ____________________.

The degrees of freedom for a test of the mean of the paired differences is the number of minus .

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:

Quiz 12: Inference About Comparing Two Populations, Part 1

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:

The symbol refers to:

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

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.

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.

The pooled variance estimator is the ____________________ average of the two sample variances.

When the population variances are unknown and unequal, we estimate each population variance with its ____________________ variance.

The test for the mean difference in a matched pairs design requires the differences to have a(n) ____________________ distribution.

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:

The unequal-variances test statistic of has an approximate ____________________ distribution with n1 + n2- 2 degrees of freedom.

If you are testing to see if a weight loss program is working, and you subtract the weights before - after for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

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

Two measurements from the same individuals is an example of data collected from a(n) ____________________ experiment.

In a matched pairs experiment the parameter of interest is the ____________________ of the population of ____________________.

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:

The pooled-variances t-test is used when the two population variances are ____________________.

The degrees of freedom for a test of the mean of the paired differences is the number of ____________________ minus ____________________.

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:

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.

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

The unequal-variances test statistic of has an approximate ____________________ distribution with n₁ + n₂- 2 degrees of freedom.

In a matched pairs experiment the parameter of interest is the of the population of .

The degrees of freedom for a test of the mean of the paired differences is the number of minus .