Exam 13: Inference About Comparing Two Populations, Part 2

The sampling distribution of the ratio of two (independent) sample variances is said to be ____________________ distributed.

If the sample sizes are large enough so the conditions are met, the difference between two sample proportions has an approximate ____________________ distribution.

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

The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that we have two ____________________ samples drawn from their respective populations.

Clinic Waiting Time: In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0. In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8. -Estimate with 95% confidence the ratio of the two population variances and interpret.

We compare two population variances by examining their ____________________.

The F-distribution can only have non-negative values.

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: -Estimate with 95% confidence the ratio of the two population variances and interpret.

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

Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.

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. -Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?

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. -Briefly describe what the interval estimate tells you.

The F-distribution is symmetric.

If the F-test statistic is large, that means the variance of Population 1 is ____________________ than/to the variance of Population 2.

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

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

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. -Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?

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

For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:

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. -Estimate with 95% confidence the difference in population proportions.