Chapter 10

Litter sizes (number of pups) for randomly chosen dogs from two breeds were compared. The sample data were entered into Excel, and the following results were produced.

-1.721

Group 1 has a mean of 13.4 and group 2 has a mean of 15.2. Both populations are known to have a variance of 9.0 and each sample consists of 18 items. What is the test statistic to test for equality of population means?

-1.800

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. To compare the two proportions, the pooled proportion is:

.132

In a test for equality of two proportions, the sample proportions were p1 = 12/50 and p2 = 18/50. The pooled proportion is:

.30

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test for equal means (assume equal variances), the critical value at α = .10 is:

1.337

John wants to compare two means. His sample statistics were Picture and Picture . Assuming equal variances, the test statistic is:

2.20

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. Assuming equal variances, the pooled variance is:

296.59

A corporate analyst is testing whether mean inventory turnover has increased. Inventory turnover in six randomly chosen product distribution centers (PDCs) is shown.

4.032

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 = .05 to see if the mean daily errors decreased significantly.

6

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:

9.00

Litter sizes (number of pups) for randomly chosen dogs from two breeds were compared. The sample data were entered into Excel, and the following results were produced.

More than .10

Mary did an analysis of acute care variances in samples of occupancy rates at two community hospitals and obtained the following results:

No, there isn't enough evidence to believe the variances are unequal.

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:

Paired t-test

A certain psychological theory predicts that men want bigger families than women. Kate asked each student in her psychology class how many children he or she considered ideal for a married couple and obtained the Excel results shown below at α = .05.

We cannot reject the hypothesis of equal population means.

Does the Speedo Fastskin II Male Hi-Neck Bodyskin competition racing swimsuit improve a swimmer's 200-yard individual medley performance times? A test of 100 randomly chosen male varsity swimmers at several different universities showed that 66 enjoyed improved times, compared with only 54 of 100 female varsity swimmers. In comparing the proportions of males versus females, is it safe to assume normality?

Yes, clearly.

In a left-tailed test comparing two means with unknown variances assumed to be equal, the test statistic was t = -1.81 with sample sizes of n1 = 8 and n2 = 12. The p-value would be:

between .025 and .05.

A new policy of "flex hours" is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. For a test comparing the two proportions, the assumption of normality for the difference of proportions is:

clearly justified.

At Huge University, a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree, compared with 120 of 800 arts and sciences seniors. We want to know if the proportion is higher in the arts and sciences group. For this test, the assumption of normality for the difference of proportions is:

clearly justified.

Two well-known aviation training schools are being compared using random samples of their graduates. It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try, compared with 104 of 260 graduates of Blue Yonder Institute. To compare the two proportions, the assumption of normality of the test statistic is:

clearly justified.

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:

independent samples t-test.

A medical researcher compared the variances in birth weights for five randomly chosen babies of each gender, with the MegaStat results shown below.

may be assumed equal at any customary α

In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 prostatectomy patients, while in Paymor Hospital such exams were given in 110 out of 200 cases. In comparing these two proportions, normality of the difference may be assumed because:

nπ ≥ 10 and n(1 - π) ≥ 10 for each sample taken separately.

Nacirema Airlines is buying a fleet of new fuel-efficient planes. The HogJet and the LitheJet both meet their price and performance needs, and both planes meet EPA noise guidelines. However, the quieter plane is preferred. Each plane is flown through a typical takeoff and landing sequence 10 times, while remote sensors at ground level record the noise levels (in decibels). The table below summarizes the sound level tests using Excel's default level of significance (α = 0.05).

realize that the decision isn't affected by our assumptions concerning the variance.

Two well-known aviation training schools are being compared using random samples of their graduates. It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try, compared with 104 of 260 graduates of Blue Yonder Institute. In a right-tailed test, the p-value is .0275, so at α = .025 we should:

reject the hypothesis of equal proportions.

A psychology researcher has a theory that predicts women will tend to carry more cash than men. 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 16 males had a mean of $17.30 with a standard deviation of $9.60. The researcher's hypothesis would lead us to perform a:

right-tailed test.