Exam 10: Two-Sample Hypothesis Tests

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:

When testing the difference between two population proportions,it is necessary to use the same size sample from each population.

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  = .10 in a two-tailed test for equal variances,the critical values are:

Mary did an analysis of acute care variances in samples of occupancy rates at two community hospitals and obtained the following results (some information is omitted). Can Mary conclude that the variances are unequal at  = .05?

In a right-tailed test comparing two proportions,the test statistic was z_calc = +1.81.The p-value is:

During a test period,an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO₂ emissions of 240 pounds per 100 miles,with a standard deviation of 20 pounds.A control group of 14 vehicles using regular gasoline showed mean CO₂ emissions of 252 pounds per 100 miles with a standard deviation of 15 pounds.A quick comparison of the sample variances suggests that the population variances are:

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  = .05. What conclusion can you draw in a two-tailed test at  = .05?

The t-test for two samples of paired data will use n differences,making it a one-sample t-test.

The critical value in an F test for equal variances is the ratio of the sample variances.

The z-test for zero difference in two means:

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

Which is not a type of comparison for which you would anticipate a two-sample test?

When the variances are known,a test comparing two independent sample means would use the normal distribution.

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).The test statistic to test the two proportions for equality would be:

In a right-tailed test comparing two means with known variances,the sample sizes were n₁ = 8 and n₂ = 12.At  = .05,the critical value would be:

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"

Of 200 youthful gamers (under 18)who tried the new Z-Box-Plus game,160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over).The pooled proportion for a test to compare the two proportions would be:

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 pass rates,find the critical value for a right-tailed test at  = .05.

When the variances are unknown,a test comparing two independent sample means would use the Student's t distribution.

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  = .05 to see if the mean daily errors decreased significantly. What would be the degrees of freedom for the appropriate test?