Exam 13: Inference About Comparing Two Populations

Random samples from two normal populations produced the following statistics: , , ,and .Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?

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 pooled proportion estimate is used when:

Two samples of sizes 25 and 20 are independently drawn from two normal populations,where the unknown population variances are assumed to be equal.The number of degrees of freedom of the equal-variances t-test statistic is 44.

When the population variances are unknown and unequal,we estimate each population variance with its ____________________ variance.

When testing vs. ,the observed value of the z-score was found to be -2.15.Then,the p-value for this test would be

Which of the following statements is false for an F-distribution?

{Aptitude Test Scores Narrative} Explain how to use the 95% confidence interval to test the hypotheses at $\alpha$ = .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} Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?

The pooled-variances t-test requires that the two population variances need not be the same.

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} Determine the rejection region for testing the equality of the two population variances at $\alpha$ = .05.

The test for the equality of two population variances is based on the:

The quantity is called the pooled variance estimate of the common variance of two unknown but equal population variances.It is the weighted average of the two sample variances,where the weights represent the:

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} Briefly explain what the interval estimate tells you.

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} Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Democrat candidate differ?

Mass Production Line A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below. -{Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations.Assume that the population variances are unknown but equal.In order to test the difference between the population means, ,the sampling distribution of the sample mean difference, ,is:

The equal-variances test statistic of is Student t-distributed with n₁ + n₂ - 2 degrees of freedom provided that the two populations are ____________________.

The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that: