Question 1

Assuming unequal variances in a t-test for a zero difference of two means,we would:

Accepted Answer

When assuming unequal variances in a t-test for a zero difference of two means, we need to calculate the degrees of freedom using a complicated formula, known as the Satterthwaite approximation. This formula takes into account the sample sizes and variances of both samples to calculate a more accurate estimate of the degrees of freedom. Simply summing the degrees of freedom for each sample or using the larger degrees of freedom for simplicity is not appropriate in this case. Additionally, using a z-test is not applicable as we are assuming unequal variances.

Question 2

In a test of a new surgical procedure,the five most respected surgeons in FlatBroke Township were invited to Carver Hospital.Each surgeon was assigned two patients of the same age,gender,and overall health.One patient was operated upon in the old way,and the other in the new way.Both procedures are considered equally safe.The surgery times are shown below: Which test should we use to test for zero difference in mean times?

Accepted Answer

A paired t-test is appropriate in this scenario as each surgeon was assigned two patients who underwent different procedures. The data is paired, and we are interested in comparing the mean surgery times between the two procedures.

Question 3

Which is not true of the two-tailed F-test for equality of variances?

Accepted Answer

The two-tailed F-test for equality of variances is not robust to nonnormality; it assumes that the populations being sampled are normally distributed.

Question 4

The folded F-test for equality of variances:

Accepted Answer

The folded F-test for equality of variances requires looking up the critical value for F1F1F1S1F1F1F10/2.

Question 5

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 6 males had a mean of $17.30 with a standard deviation of $9.60.At $\alpha$ = .10,to test for equal variances in a two-tailed test,the critical values are:

Accepted Answer

The answer of A random sample of Ersatz University students...

Question 6

Which of the following is not a characteristic of the F distribution?

Accepted Answer

The F distribution describes the ratio of two sample variances, not two sample means.

Question 7

The table below shows the mean number of daily errors by seven air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors have decreased from Week 1 to Week 2. The right-tailed critical value at $\alpha$ = 0.05 is:

Accepted Answer

We need to find the critical value for a right-tailed paired t-test at F1F1F1S1F1F1F10 = 0.05 with 6 degrees of freedom (n-1=7-1). Using a t-distribution table or a calculator, we find the critical value to be 1.943. Therefore, the correct answer is B.

Question 8

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs)is shown. The right-tailed critical value at $\alpha$ = 0.005 is:

Accepted Answer

Since we are testing whether there is an increase in mean inventory turnover, we use a right-tailed test. The degrees of freedom for the numerator is 5 (number of PDCs - 1) and the degrees of freedom for the denominator is also 5. Using the F-distribution table, the critical value at a significance level of 0.005 and degrees of freedom of 5 for the numerator and denominator is 4.032. Therefore, the answer is C.

Question 9

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.Random samples of 5 babies' weights (pounds)for each gender showed the following: To test the researcher's hypothesis,we should use the:

Accepted Answer

The researcher is comparing the mean birth weight of two independent groups (boys and girls), so an independent samples t-test should be used. The paired (dependent) samples t-test would be appropriate if the researcher was comparing the same group of babies at two different time points (before and after), for example. The large-sample z-test would be appropriate if the sample size was very large, but in this case, both samples have n=5, which is relatively small. The t-test for correlation would be appropriate if the researcher was examining the relationship between two continuous variables.

Question 10

An F-test for equality of variances gives a p-value of .003.At $\alpha$ = .05,what conclusion can be made about the preferred test to compare the means for the same sample?

Accepted Answer

A low p-value from an F-test for equality of variances implies that the assumption of equal variances may be violated, so it would not be appropriate to pool the variances in a t-test for equality of means. Therefore, we would not choose a pooled variance t-test, and options A and C can be ruled out. D is incorrect because the variances do have an impact on the t-test for equality of means, as the calculation of the test statistic involves dividing the difference in means by the standard error, which depends on the variances of the two groups.

Question 11

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs)is shown. The value of the test statistic is:

Accepted Answer

The answer of A corporate analyst is testing whether mean...

Question 12

The F-test for equality of variances assumes:

Accepted Answer

The F-test for equality of variances assumes normal populations, regardless of the means and sample sizes.

Question 13

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 6 males had a mean of $17.30 with a standard deviation of $9.60.The value of the test statistic for a folded F-test for equal variances is:

Accepted Answer

The formula for the test statistic for a folded F-test for equal variances is:

$\frac{s_1^2}{s_2^2} = \frac{	ext{larger sample variance}}{	ext{smaller sample variance}}$

In this case, the larger sample is the one with the smaller variance, which is the male group. So, we have:

$\frac{s_{male}^2}{s_{female}^2} = \frac{9.60^2}{3.20^2} \approx 9.00$

Therefore, the value of the test statistic is 9.00, which corresponds to choice (C).

Question 14

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors decreased significantly. The test statistic is:

Accepted Answer

The answer of The table below shows the mean number...

Question 15

In a test of a new surgical procedure,the five most respected surgeons in FlatBroke Township were invited to Carver Hospital.Each surgeon was assigned two patients of the same age,gender,and overall health.One patient was operated upon in the old way,and the other in the new way.Both procedures are considered equally safe.The surgery times are shown below: The time (in minutes)to complete each procedure was carefully recorded.In a right-tailed test for a difference of means,the test statistic is:

Accepted Answer

The test statistic for a right-tailed test for a difference of means using a t-distribution is calculated as (x1̄-x2̄-D0)/(sqrt((s1^2/n1)+(s2^2/n2))), where x1̄ and x2̄ are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and D0 is the hypothesized difference between the population means (in this case, D0 = 0 because there is no expected difference between the old and new procedures). With a significance level of 0.05 and 8 degrees of freedom (5 surgeons * 2 patients - 2), the critical t-value is 1.860 (found using a t-table or calculator). Plugging in the values from the data, the test statistic is (35.8-43.2-0)/(sqrt((23.0^2/10)+(26.3^2/10))) = -3.162, which is less than the critical t-value. Therefore, we reject the null hypothesis of no difference between the old and new procedures and conclude that there is a statistically significant difference in the surgery times.

Question 16

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs)is shown. The degrees of freedom for the appropriate test would be:

Accepted Answer

The appropriate test for testing whether mean inventory turnover has increased is a one-sample t-test. Since six PDCs were randomly chosen, the sample size is 6. The degrees of freedom for a one-sample t-test with a sample size of 6 is 5 (df=n-1). Therefore, the correct answer is B.

Question 17

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the variance in the time it takes to perform an appendectomy.A sample of 8 appendectomies using the old method had a variance of 36 minutes,while a sample of 10 appendectomies using the experimental method had a variance of 16 minutes.At$\alpha$ = .10 in a two-tailed test for equal variances,the critical values are:

Accepted Answer

Using the F-distribution table with 7 degrees of freedom in the numerator and 9 degrees of freedom in the denominator (the smaller sample size minus 1), and alpha level of .10 (two-tailed), the critical values are 0.272 and 3.29. Therefore, the best choice is A.

Question 18

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.A random sample of babies' weights (pounds)showed the following. How many degrees of freedom would be used to test for a zero difference in means?

Accepted Answer

The degrees of freedom for a two-sample t-test is calculated as the sum of the sample sizes of both groups minus 2. If the sample sizes are not provided, the degrees of freedom cannot be determined. However, assuming equal sample sizes of 5 for each group (as implied by choice B), the degrees of freedom would be 5 + 5 - 2 = 8.

Question 19

Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results. Which conclusion is correct in a two-tailed test at $\alpha$ = .05?

Accepted Answer

The p-value is greater than 0.05, so we fail to reject the null hypothesis.

Question 20

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors decreased significantly. What would be the degrees of freedom for the appropriate test?

Accepted Answer

The degrees of freedom for a paired t-test is n-1, where n is the number of pairs of data. In this case, there are 7 pairs of data, so the degrees of freedom is 7-1 = 6.

Quiz 10: Two-Sample Hypothesis Tests

Assuming unequal variances in a t-test for a zero difference of two means,we would:

Which is not true of the two-tailed F-test for equality of variances?

The folded F-test for equality of variances:

Which of the following is not a characteristic of the F distribution?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The right-tailed critical value at $\alpha$ = 0.005 is:

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.Random samples of 5 babies' weights (pounds) for each gender showed the following: To test the researcher's hypothesis,we should use the:

An F-test for equality of variances gives a p-value of .003.At $\alpha$ = .05,what conclusion can be made about the preferred test to compare the means for the same sample?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The value of the test statistic is:

The F-test for equality of variances assumes:

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 6 males had a mean of $17.30 with a standard deviation of $9.60.The value of the test statistic for a folded F-test for equal variances is:

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors decreased significantly. The test statistic is:

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The degrees of freedom for the appropriate test would be:

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.A random sample of babies' weights (pounds) showed the following. How many degrees of freedom would be used to test for a zero difference in means?

Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results. Which conclusion is correct in a two-tailed test at $\alpha$ = .05?

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors decreased significantly. What would be the degrees of freedom for the appropriate test?

Quiz 10: Two-Sample Hypothesis Tests

Assuming unequal variances in a t-test for a zero difference of two means,we would:

Which is not true of the two-tailed F-test for equality of variances?

The folded F-test for equality of variances:

Which of the following is not a characteristic of the F distribution?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The right-tailed critical value at α\alphaα = 0.005 is:

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.Random samples of 5 babies' weights (pounds) for each gender showed the following: To test the researcher's hypothesis,we should use the:

An F-test for equality of variances gives a p-value of .003.At α\alphaα = .05,what conclusion can be made about the preferred test to compare the means for the same sample?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The value of the test statistic is:

The F-test for equality of variances assumes:

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 6 males had a mean of $17.30 with a standard deviation of $9.60.The value of the test statistic for a folded F-test for equal variances is:

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at α\alphaα = .05 to see if the mean daily errors decreased significantly. The test statistic is:

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The degrees of freedom for the appropriate test would be:

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies.A random sample of babies' weights (pounds) showed the following. How many degrees of freedom would be used to test for a zero difference in means?

Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results. Which conclusion is correct in a two-tailed test at α\alphaα = .05?

A corporate analyst is testing whether mean inventory turnover has increased.Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown. The right-tailed critical value at $\alpha$ = 0.005 is:

An F-test for equality of variances gives a p-value of .003.At $\alpha$ = .05,what conclusion can be made about the preferred test to compare the means for the same sample?

The table below shows the mean number of daily errors by air traffic controller trainees during the first two weeks on the job.We want to perform a paired t-test at $\alpha$ = .05 to see if the mean daily errors decreased significantly. The test statistic is:

Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results. Which conclusion is correct in a two-tailed test at $\alpha$ = .05?