Exam 13: Inference About Comparing Two Populations

If you are testing to see if a weight loss program is working, and you subtract the weights after - before for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

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

The equal-variances test statistic of is Student t-distributed with n₁ + n₂ degrees of freedom, provided that the two populations are normal.

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} Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?

For testing the difference between two population proportions, the pooled proportion estimate is found by taking:

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.

The F-distribution is the sampling distribution of the ratio of:

Worker Safety An OSHA agent wanted to determine if efforts to promote safety have been successful.By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year.A random sample of 400 workers last year revealed that 80 suffered some form of injury. -{Worker Safety Narrative} Estimate with 95% confidence the difference in population proportions.

The variance of the difference between two sample proportions equals the ____________________ of their population proportion variances.

Additives A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive 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 -{Additives Narrative} State the null and alternative hypotheses to determine if the average number of hours until spoilage begins differs for the additives A and B.