Exam 10: Two-Sample Hypothesis Tests

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, the p-value for a right-tailed test is approximately:

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

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

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 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:

The F distribution is never negative and is always skewed right.

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 of equal means (assume equal variances), the pooled variance is:

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. At α = 0.05, in a left-tailed test, the critical value to compare the means (assuming equal variances) is:

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 p-value for a left-tailed test is approximately:

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:

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. Hypothesis Test: Independent Groups (t-test, unequal variance) Men Women 2.812 2.1538 mean 1.2505 0.5547 std. dev. 11 13 sample size 13 pooled df $0.6582$ $\quad$$\quad$ difference (Men - Women) $0.40722$ $\quad$$\quad$ standard error of difference 0 $\quad$$\quad$$\quad$$\quad$$\quad$ hypothesized difference $1.62$$\quad$$\quad$$\quad$$\quad$ t $0.065$$\quad$$\quad$$\quad$$\quad$ P-value (one-tailed, upper) F-test for equality of variance 1.56375 variance: Men $0.307692$ $\quad$ variance: Women $5.08$$\quad$ F $0.01$$\quad$ P-value What conclusion can you draw from this analysis at ? = .05?

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. p1 p2 0.15 0.12 (as decimal) 120/800 144/1200 (as fraction) 120. 144. 800 1200 0.03 sample difference 0.00 hypothesized difference 0.01545 std. error x.xx z .0522 p-value (two-tailed) At ? = .05, the two-tailed test for a difference in proportions is:

The folded F-test for equality of variances:

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:

Mary did an analysis of acute care variances in samples of occupancy rates at two community hospitals and obtained the following results: F-test for equality of variance 108.243 variance: group 1 98.371 variance: group 2 1.100 F 0.905 p-value Can Mary conclude that the variances are unequal at ? = .05?

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

Random samples of Tuesday and Friday withdrawals from a college-campus ATM were compared to see whether or not there was a difference in the means. The results shown below are from MegaStat. Analyze these results thoroughly. Hypothesis Test: Independent Groups (t-test, unequal variance) Friday Tuesday 82.40 41.00 mean 75.35 35.53 std.dev. 25 20 n $35$$\quad$$\quad$$\quad$ df $41.400$ $\quad$ difference (Friday - Tuesday) $17.035$ $\quad$ standard error of difference 0 $\quad$$\quad$$\quad$ hypothesized difference $2.430$$\quad$$\quad$ t $.0204$$\quad$ p-value (two-tailed)

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 p-value is:

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:

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. p1 p2 0.15 0.12 (as decimal) 120/800 144/1200 (as fraction) 120. 144. 800 1200 0.03 sample difference 0.00 hypothesized difference 0.01545 std. error x.xx z .0522 p-value (two-tailed) The test statistic (shown as z = x.xx) is approximately: