Exam 13: Inference About Comparing Two Populations

In comparing two population means of interval data,we must decide whether the samples are independent (in which case the parameter of interest is )or matched pairs (in which case the parameter is μ_D)in order to select the correct test statistic.

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

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:

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

The pooled-variances t-test requires that the two population variances need not be the same.

All F-tests for the equality of two population variances are one-tailed tests.

The symbol refers to:

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

Clothing Expenditures A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.He believed that the husband's perception would be higher than the wife's.To judge his belief,he takes a random sample of ten married couples and asks each spouse to estimate the family clothing expenditure (in dollars)during the previous month.The data are shown below. ​ ​ -{Clothing Expenditures Narrative} Can the consultant conclude at the 5% significance level that the husband's estimate is higher than the wife's estimate?

In testing for the equality of two population variances,when the populations are normally distributed,the 10% 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:

Additives A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive 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 ​ ​ -{Additives Narrative} State the null and alternative hypotheses to determine if the average number of hours until spoilage begins differs for the additives A and B.

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} Determine the rejection region for testing the equality of the two population variances at α = .05.

If there are 10 pairs of data in a matched pairs experiment,the degrees of freedom for the corresponding t-test is 18.

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} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.

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?

Unless we can conclude that the population variances are equal,we cannot use the pooled variance estimate.

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 pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.

Additives A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive 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 ​ ​ -{Additives Narrative} Determine the rejection region at α = .05 and write the proper conclusion.

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