Exam 13: Inference About Comparing Two Populat

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} Can we infer at the 99% significance level that the proportion of Canadians and Americans who believe that there is too much sex on television differ?

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} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.

The F -distribution is symmetric.

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

The pooled proportion estimate is used when:

Pooling is made possible by hypothesizing (under the null hypothesis)that p ₁ __________ p ₂.

The F -test used for testing the difference in 2 population variances is always a one-tailed test.

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.

Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: {Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

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

In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always\sometimes\never)pool the population proportions.

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

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n ₁ p ₁ ³ 30 and n ₂ p ₂ ³ 30.

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?

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

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

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} What is the p -value of the test?

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.

Fitness Program A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program. However, he will not perform the equal-variance t -test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: {Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?

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