Exam 13: Inference About Comparing Two Populations

The t-test for the difference between the means of two independent populations assumes that the respective:

The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.

Pooling is made possible by hypothesizing (under the null hypothesis)that p₁ __________ p₂.

We use a t-test to determine whether two population variances are equal.

Starting Salary In testing the hypotheses vs. ,two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): , , , , ,and .(Assume the salaries have normal distributions. ) -{Starting Salary Narrative} What conclusion can we draw at the 5% significance level?

The pooled-variances t-test is used when the two population variances are ____________________.

A political analyst in Iowa surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of ____________________ samples.

Two measurements from the same individuals is an example of data collected from a(n)____________________ experiment.

Promotional Campaigns The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness,the executive records the daily gross sales (in $1,000s)in one restaurant during the campaign and during the week after the campaign ends.The data is shown below. -{Promotional Campaigns Narrative} Estimate with 95% confidence the mean difference and interpret.

Senatorial Election A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate. -{Senatorial Election Narrative} Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.

Speed Limits Violation Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state.A random sample of the speeds of 2,500 randomly selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit.The data follow. -{Speed Limits Violation Narrative} Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level?

In testing for the equality of two population variances,when the populations are normally distributed,the 5% level of significance has been used.To determine the rejection region,it will be necessary to refer to the F table corresponding to an upper-tail area of .05.

Profit Margin An investor is considering two types of investment.She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2.However,she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2.To help make her decision,she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2.She finds that the sample variances of Investments 1 and 2 are 225 and 118,respectively. -{Profit Margin Narrative} Briefly describe what the interval estimate tells you.

When testing for the equality of two population variances the number in the null hypothesis is ____________________.

Antioxidants A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below -{Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.

Unless we can conclude that the population variances are equal,we cannot use the pooled variance estimate.

TV Sex A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television.In a survey of 1,500 Americans,810 believe that there is too much television sex. -{TV Sex Narrative} Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.

Which of the following statements is correct regarding the percentile points of the F-distribution?

In constructing a confidence interval estimate for the difference between two population proportions,we pool the population proportions when the populations are normally distributed.

All F-tests for the equality of two population variances are one-tailed tests.