Exam 10: Two-Sample Hypothesis Tests

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 ( = 0.05). After inspecting this table,we would most likely:

Randomly chosen MBA students were asked their opinions about the ideal number of children for a married couple.The sample data were entered into MegaStat,and the following results were produced. What conclusion can you draw from this analysis at  = .05?

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 test statistic for the researcher's hypothesis is:

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.What is the test statistic to test for a zero difference in the population proportions?

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 a left-tailed test for equality of proportions,the test statistic is:

A confidence interval for the difference of two population means:

If the sample proportions were p₁ = 12/50 and p₂ = 18/50,the 95 percent confidence interval for the difference of the population proportions is approximately:

The Welch-Satterthwaite t-test for two means has the same degrees of freedom as the pooled samples t-test for two means.

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.The test statistic to test the pass rates for equality is:

Randomly chosen MBA students were asked their opinions about the ideal number of children for a married couple.The sample data were entered into MegaStat,and the following results were produced. To compare the means,would it be appropriate to use a test that assumes equal variances?

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:

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

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.The pooled proportion for this test is:

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

The Welch-Satterthwaite test is more conservative than the pooled variance test to compare two population means with unknown variances in independent samples.

A paired t-test with two columns of 8 observations in each column would use d.f.= 7.

Based on a random sample of 13 tire changes,the mean time to change a tire on a Boeing 777 has a mean of 59.5 minutes with a standard deviation of 8.4 minutes.For 10 tire changes on a Boeing 787 the mean time was 64.3 minutes with a standard deviation of 12.4 minutes.To test for equal variances in a two-tailed test at  = .10,the critical values are:

John wants to compare two means.His sample statistics were and .Assuming equal variances,the degrees of freedom for his test will be:

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.MegaStat's results for a two-tailed test are shown below. At  = .05,the two-tailed test for a difference in proportions is:

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 ( = 0.05). In a left-tailed test comparing the means at  = .05,we would: