Exam 13: Inference About Comparing Two Populations

In comparing the difference in means with a matched pairs experiment,the variable under consideration is ,where the subscript D refers to the difference.

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} Estimate with 95% confidence the population mean difference.

Undergraduates' Test Scores 35 undergraduate students who completed two years of college were asked to take a basic mathematics test.The mean and standard deviation of their scores were 75.1 and 12.8,respectively.In a random sample of 50 students who only completed high school,the mean and standard deviation of the test scores were 72.1 and 14.6,respectively. -{Undergraduates' Test Scores Narrative} Can we infer at the 10% significance level that a difference exists between the two groups?

{Aptitude Test Scores Narrative} Estimate with 95% confidence the difference between the two population means.

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} Estimate with 90% confidence the difference between the two population proportions.

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} Estimate with 95% confidence the difference between the two population means.

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

The service manager of a car dealer wants to determine if owners of new cars (two years old or less)tune up their cars more frequently than owners of older cars (more than two years old).From his records he takes a random sample of ten new cars and ten older cars and determines the number of times the cars were tuned up in the last 12 months.The data follow.Do these data allow the service station owner to infer at the 10% significance level that new car owners tune up their cars more frequently than older car owners?

Undergraduates' Test Scores 35 undergraduate students who completed two years of college were asked to take a basic mathematics test.The mean and standard deviation of their scores were 75.1 and 12.8,respectively.In a random sample of 50 students who only completed high school,the mean and standard deviation of the test scores were 72.1 and 14.6,respectively. -{Undergraduates' Test Scores Narrative} Estimate with 90% confidence the difference in mean scores between the two groups of students.

The variance of the difference in sample proportions equals the difference of their population variances.

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2,the second observation of sample 1 with the second observation of sample 2,and so on,the samples are referred to as:

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

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment.If the paired differences are normal,then the distribution used for testing is the:

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} Calculate the value of the test statistic for testing the equality of the population variances,and write the proper conclusion.

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

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

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

The statistical distribution used for testing the difference between two population variances is the

The expected value of the difference of two sample means equals the difference of the corresponding population means when:

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