Exam 10: Two-Sample Hypothesis Tests

The F-test for equality of variances assumes:

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.What is the z test statistic?

When sample data occur in pairs,an advantage of choosing a paired t-test is that it tends to increase the power of a test,as compared to treating each sample independently.

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?

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:

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). If we switched from  = .05 to  = .005 in a two-tailed test of means,our assumption about variances (assumed equal or assumed unequal)would:

The folded F-test for equality of variances:

John wants to compare two means.His sample statistics were and .Assuming equal variances,the 95 percent confidence interval for the difference of the population means 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 p-value for a right-tailed test to compare the two proportions would be approximately:

The table below shows two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. At  = .05,can you conclude that the first sample has a larger variance than the second sample?

The degrees of freedom for the t-test used to compare two population means (independent samples)with unknown variances (assumed equal)will be n₁ + n₂ - 2.

In comparing the means of two independent samples,if the test statistic indicates a significant difference at  =.05,it will also be significant at  = .10.

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 95 percent confidence interval for the difference of proportions would be approximately:

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

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?

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

If the sample proportions are p₁ = 6/90 and p₂ = 4/100,normality may be assumed in a test comparing the two population proportions.

A pooled proportion is calculated by giving each sample proportion an equal weight.

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