Question 1

In comparing two population means of interval data,we must decide whether the samples are independent (in which case the parameter of interest is )or matched pairs (in which case the parameter is $\mu$_D)in order to select the correct test statistic.

Accepted Answer

This statement is true as the choice of test statistic (either the independent samples t-test or paired samples t-test) depends on whether the samples are independent or matched pairs.

Question 2

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:

Accepted Answer

In a matched pairs experiment, each pair provides one data point, resulting in n=10 data points. However, since the pairs are matched, the variability due to individual differences within the pairs is removed. This reduces the effective sample size to n-1, or 10-1=9 degrees of freedom.

Question 3

In testing the hypothesis  vs.  ,two random samples from two normal populations produced the following statistics:  .What conclusion can we draw at the 1% significance level?

Accepted Answer

The answer of In testing the hypothesis  vs. ...

Question 4

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:

Accepted Answer

Matched pairs refer to samples in which each observation in one sample is matched or paired with a corresponding observation in the other sample, based on some natural relationship between the pairs (such as before-and-after measurements or measurements on identical twins). In contrast, independent samples do not have such a natural relationship between the observations in each sample. Nonrandom samples refers to samples that are not randomly selected from the population of interest.

Question 5

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 6

If you are testing to see if a weight loss program is working,and you subtract the weights before -fter 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 7

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:

Accepted Answer

When the paired differences are normal, the distribution used for testing is the Student t-distribution.

Question 8

When comparing two population means using data that are gathered from a matched pairs experiment,the test statistic for $\mu$_D is Student t-distributed with v = n_D -1 degrees of freedom,provided that the differences are normally distributed.

Accepted Answer

This statement is true. According to the principles of matched pairs experiments, we are comparing the means of two populations with dependent samples. Therefore, we use the t-test for paired samples. The test statistic for the t-test is Student t-distributed with v = n-1 degrees of freedom, where n is the number of pairs. In this case, the formula for the test statistic includes the difference between the means, which is divided by the standard error of the differences. If the differences are normally distributed, then the t-test is appropriate and the test statistic follows a Student t-distribution with the specified degrees of freedom.

Question 9

A Marine boot camp instructor recorded the time in which each of 15 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 15 degrees of freedom.

Accepted Answer

The instructor would use a t-distribution with 14 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, 15 recruits), so 15 - 1 = 14.

Question 10

The number of degrees of freedom associated with the t-test,when the data are gathered from a matched pairs experiment with 8 pairs,is 7.

Accepted Answer

In a matched pairs experiment, the degrees of freedom for the t-test is equal to the number of pairs minus 1, which in this case is 8-1 = 7. Therefore, the statement is true.

Question 11

The symbol  refers to:

Accepted Answer

The answer of The symbol  refers to:
...

Question 12

Promotional Campaigns
The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness,the executive records the daily gross sales (in $1,000s)in one restaurant during the campaign and during the week after the campaign ends.The data is shown below.
 
-{Promotional Campaigns Narrative} Estimate with 95% confidence the mean difference and interpret.

Accepted Answer

The answer of Promotional Campaigns
The general manager of a chain...

Question 13

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 14

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 15

Promotional Campaigns
The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness,the executive records the daily gross sales (in $1,000s)in one restaurant during the campaign and during the week after the campaign ends.The data is shown below.
 
-{Promotional Campaigns Narrative} Can they infer at the 5% significance level that sales increase during the campaign?

Accepted Answer

The answer of Promotional Campaigns
The general manager of a chain...

Question 16

If there are 10 pairs of data in a matched pairs experiment,the degrees of freedom for the corresponding t-test is 18.

Accepted Answer

The degrees of freedom for a matched pairs t-test is equal to the number of pairs minus one, which in this case would be 10-1=9.

Question 17

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 18

Engine Wear
To compare the wearing of two types of automobile engines,1 and 2,an experimenter chose to "pair" the measurements,comparing the wear for the two types of engines on each of 7 automobiles,as shown below.
 
-{Engine Wear Narrative} Estimate with 90% confidence the mean difference and interpret.

Accepted Answer

The answer of Engine Wear
To compare the wearing of two...

Question 19

If you are testing to see if a weight loss program is working,and you subtract the weights after - before 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 20

Engine Wear
To compare the wearing of two types of automobile engines,1 and 2,an experimenter chose to "pair" the measurements,comparing the wear for the two types of engines on each of 7 automobiles,as shown below.
 
-(Engine Wear Narrative} Determine whether these data are sufficient to infer at the 10% significance level that the two types of engines wear differently.

Accepted Answer

The answer of Engine Wear
To compare the wearing of two...

Quiz 13: Inference About Comparing Two Populations

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:

In testing the hypothesis vs. ,two random samples from two normal populations produced the following statistics: .What conclusion can we draw at the 1% significance level?

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

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

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:

When comparing two population means using data that are gathered from a matched pairs experiment,the test statistic for $\mu$ _D is Student t-distributed with v = n_D -1 degrees of freedom,provided that the differences are normally distributed.

A Marine boot camp instructor recorded the time in which each of 15 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 15 degrees of freedom.

The number of degrees of freedom associated with the t-test,when the data are gathered from a matched pairs experiment with 8 pairs,is 7.

The symbol refers to:

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 .

If there are 10 pairs of data in a matched pairs experiment,the degrees of freedom for the corresponding t-test is 18.

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

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

Quiz 13: Inference About Comparing Two Populations

In comparing two population means of interval data,we must decide whether the samples are independent (in which case the parameter of interest is )or matched pairs (in which case the parameter is μ\muμ D)in order to select the correct test statistic.

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:

In testing the hypothesis vs. ,two random samples from two normal populations produced the following statistics: .What conclusion can we draw at the 1% significance level?

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

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

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:

When comparing two population means using data that are gathered from a matched pairs experiment,the test statistic for μ\muμ D is Student t-distributed with v = nD -1 degrees of freedom,provided that the differences are normally distributed.

A Marine boot camp instructor recorded the time in which each of 15 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 15 degrees of freedom.

The number of degrees of freedom associated with the t-test,when the data are gathered from a matched pairs experiment with 8 pairs,is 7.

The symbol refers to:

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 ____________________.

If there are 10 pairs of data in a matched pairs experiment,the degrees of freedom for the corresponding t-test is 18.

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

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

When comparing two population means using data that are gathered from a matched pairs experiment,the test statistic for $\mu$ _D is Student t-distributed with v = n_D -1 degrees of freedom,provided that the differences are normally distributed.

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 .