Exam 13: Inference About Comparing Two Populations

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

Starting Salary In testing the hypotheses vs. , 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): , , , , , and .(Assume the salaries have normal distributions.) -{Starting Salary Narrative} What conclusion can we draw at the 5% significance level?

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

Headache Medicine A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness.In testing the hypotheses vs. , the following statistics were obtained: n₁ = 400, x₁ = 208, n₂ = 250, and x₂ = 115, where x₁ and x₂ represent the number of patients in the two samples (men vs.women) who reported to have drowsiness as a result of taking headache medicine. -{Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference is normal if the sample sizes are both greater than 30.

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.

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?

The best estimator of the difference between two population means is the difference between two sample means .

Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown).In order to test the difference between the population means, the test statistic is:

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:

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} Develop the 95% confidence interval estimate of the ratio of the two population variances.

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

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. -{Clinic Waiting Time Narrative} Can we infer at the 5% level of significance that the population variances differ?

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

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

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

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

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

Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions to assess the cost of repairs.An insurance executive is concerned that different appraisers produce significantly different assessments.In an experiment 10 motorcycles that have recently been involved in accidents were shown to two appraisers.Each assessed the estimated repair costs.These results are shown below.Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 8 pairs, is 7.