Exam 13: Inference About Comparing Two Populations

Promotional Campaigns The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness,the executive records the daily gross sales (in $1,000s)in one restaurant during the campaign and during the week after the campaign ends.The data is shown below. -{Promotional Campaigns Narrative} Can they infer at the 5% significance level that sales increase during the campaign?

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?

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 $\mu$ _D)in order to select the correct test statistic.

In comparing two population means the statistic under consideration is .

The degrees of freedom for a test of the mean of the paired differences is the number of ____________________ minus ____________________.

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: . -{Aptitude Test Scores Narrative} Test at the 5% significance level to determine whether we can infer that the two population means differ.

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:

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?

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?

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:

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

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

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations,we:

The test statistic for testing for the equality of two population variances has a(n)____________________ distribution.

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} Briefly describe what the interval estimate tells you.

When testing for the difference between two population variances with sample sizes of n₁ = 8 and n₂ = 10,the degrees of freedom are:

In constructing a confidence interval estimate for the difference between two population proportions,we ____________________ (always/sometimes/never)pool the population proportions.

When testing the equality of two population variances the number in the null hypothesis is 0.

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} Explain how to use the 95% confidence interval to test the hypotheses at $\alpha$ = .05.

In a matched pairs experiment the parameter of interest is the ____________________ of the population of ____________________.