Exam 13: Inference About Comparing Two Populations

NARRBEGIN: Anioxidants 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 Antioxdeant A Antioxadant B Sample Mean 108.7 hours 98.7 hours Sample Standard Deviation 10.5 hours 13.6 hours NARREND -{Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at $\alpha$ = 0.05.

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

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

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

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

When the data from two populations are ____________________ the parameter to be tested and estimated is the difference between the two population proportions.

NARRBEGIN: Starting Salary Starting Salary In testing the hypotheses $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { 1 } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ , two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): $n _ { 1 } = 50$ , $\bar { x } _ { 1 } = 35$ , $s _ { 1 } = 28$ , $n _ { 2 } = 50$ , $\bar { x } _ { 2 } = 30$ , and $s _ { 2 } = 10$ . (Assume the salaries have normal distributions.) NARREND -{Starting Salary Narrative} Estimate with 95% confidence the difference between the two population means.

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

NARRBEGIN: Speed Limits Violation 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. In State Cars Out af State Cars Speeding 521 328 Nat speeding 1141 510 NARREND -{Speed Limits Violation Narrative} Briefly describe what the interval estimate tells you.

NARRBEGIN: Worker Safety 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.NARREND -{Worker Safety Narrative} Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?

Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal. The sampling distribution of the ratio of the two sample variances is:

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

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.

NARRBEGIN: Aptitude Test Scores Aptitude Test Scores Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are normally distributed (total points = 100). The following statistics regarding their scores in an aptitude test were obtained: $\bar { x } _ { 1 } = 76 , s _ { 1 } = 8 , \bar { x } _ { 2 } = 72 , \text { and } s _ { 2 } = 6.5$ .NARREND -{Aptitude Test Scores Narrative} Explain how to use the 95% confidence interval to test the hypotheses at $\alpha$ = .05.

The symbol $\bar { x } _ { D }$ refers to:

The expected value of the difference between two sample proportions is the ____________________ of/between their corresponding population proportions.

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

If we are testing for the difference between the means of two independent populations with equal variances, samples of n₁ = 15 and n₂ = 15 are taken, then the number of degrees of freedom is equal to

NARRBEGIN: Anioxidants 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 Antioxdeant A Antioxadant B Sample Mean 108.7 hours 98.7 hours Sample Standard Deviation 10.5 hours 13.6 hours NARREND -{Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.

The ratio of two independent chi-squared variables divided by their degrees of freedom is: