Exam 13: Inference About Comparing Two Populations

The F-distribution is symmetric.

When the sample sizes are equal, the pooled variance of the two samples is the weighted average of the two sample variances.

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

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

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 of the program data follow: -{Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

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?

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

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} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.

When we test for differences between the means of two independent populations, we can only use a two-tailed test.

Both the equal-variances and unequal variances test statistic and confidence interval estimator of require that the two populations be normally distributed.

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} What is the p-value of the test? Explain how to use it for testing the hypotheses.

The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.

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.

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.

Suppose we randomly selected 250 people, and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:

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.

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 of the program data follow: -{Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?

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?

The test statistic for testing for the equality of two population variances has an F-distribution with ____________________ and ____________________ degrees of freedom.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom is: