Exam 10: Statistical Inference Concerning Two Populations

We convert the estimate into the corresponding value of the z or t test statistic by dividing the difference between and the hypothesized difference by the standard error of the estimator .

Do men really spend more money on St.Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54.Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25,respectively.Which of the following is the correct value of test statistic?

A new sales training program has been instituted at a rent-to-own company.Prior to the training,10 employees were tested on their knowledge of products offered by the company.Once the training was completed,the employees were tested again in an effort to determine whether the training program was effective.Scores are known to be normally distributed.The sample scores on the tests are listed next.Use pretest score as µ₁ for population 1 and posttest score as µ₂ for population 2,orµ_D as the difference calculated as pretest score minus posttest score.Pretest Score Which of the following is the correct conclusion for the test at α = 0.05?

A restaurant chain has two locations in a medium-sized town and,believing that it has oversaturated the market for its food,is considering closing one of the restaurants.The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway.The CEO of this company,wishing to test this claim,randomly selects 36 monthly revenue totals for each restaurant.The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000,while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000.Assume there is no reason to believe the population standard deviations are equal,and let μ₁ and μ₂ denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway,respectively.Which of the following is the appropriate critical value(s)to test the manager's claim at the 5% significance level?

A new study has found that,on average,6- to 12-year-old children are spending less time on household chores today compared to 1981 levels.Suppose two samples representative of the study's results report the following summary statistics for the two periods. Which of the following is the correct value of the test statistic assuming that the unknown population variances are equal?

If the hypothesized difference d₀ is ______,then the value of the test statistic is computed as

A recent study from the University of California,Berkeley,suggests that,compared to white Americans,black Americans are more likely to cross the race barrier in online dating.In a sample of 120 white men,24 initiated contact with someone outside their race,whereas in a similar sample of 90 black men,36 initiated contact with someone outside their race. a.Specify the hypotheses to justify the suggestion. b.Find the critical value(s)of the appropriate test at the 1% significance level. c.Calculate the value of the test statistic. d.Make a conclusion at the 1% significance level.

A student has to decide whether he wants to major in electrical engineering or computer science.To find out which job pays more,he interviews eight alumni in each profession and asks them what their starting salary was.The electrical engineering alumni had a mean starting salary of $54,000 and a standard deviation of $8,000.The computer science alumni had a mean starting salary of $62,000 and a standard deviation of $10,000.It is reasonable to assume equal population variances,and assume starting salaries are normally distributed. a.Specify the competing hypotheses to determine if electrical engineering and computer science majors mean starting salaries are equal. b.Calculate the value of the test statistic and find the critical value at a 5% significance level. c.Make a conclusion at the 5% significance level.

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season.The first variety is milk chocolate while the second is milk chocolate filled with mint.It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances.Two independent samples of 18 observations each are collected for the holiday period.A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million.A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million.Use milk chocolate as population 1 and mint chocolate as population 2.Assuming the population variances are equal,which of the following is the value of the appropriate test statistic?

When testing the difference between two population means under independent sampling,we use the z distribution if _________ .

A tutor promises to improve GMAT scores of students by more than 50 points after three lessons.To see if this is true,the tutor takes a sample of 49 students' test scores after and before they received tutoring.The mean difference was 53 points better after tutoring,with a standard deviation of the difference equal to 12 points.Let µ_D denote the mean of the difference: score after tutoring minus score before tutoring.Which of the following hypotheses will determine if the students improved their test scores by more than 50 points after being tutored?

The student senate at a local university is about to hold elections.A representative from the women's sports program and a representative from the men's sports program must both be elected.Two candidates,an incumbent and a challenger,are vying for each position and early polling results are presented next.A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates.In a sample of 100 voters,67 said that they would vote for the women's incumbent candidate.In a separate sample of 100 voters,55 said they would vote for the men's incumbent candidate.Let p₁ and p₂ be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs,respectively.Use a 5% level of significance.Which of the following is(are)critical value(s)of the appropriate test?

A tutor promises to improve GMAT scores of students by more than 50 points after three lessons.To see if this is true,the tutor takes a sample of 49 students' test scores after and before they received tutoring.The mean difference was 53 points better after tutoring,with a standard deviation of the difference equal to 12 points.Let µ_D denote the mean of the difference: score after tutoring minus score before tutoring.Assuming α = 0.05,which of the following is the appropriate critical value?

A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP)modifications,where the federal government pays the bank $1,000 for each successful modification,and non-HAMP modifications,where the bank does not receive a bonus from the federal government.To qualify for a HAMP modification,borrowers must meet a set of financial suitability criteria.Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications.Let p₁ and p₂ represent the proportion of borrowers who received HAMP modifications that did not re-default,and the proportion of borrowers who received non-HAMP modifications that did not re-default,respectively.

Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population,using independent random sampling?

A demographer wants to measure life expectancy in countries 1 and 2.Let and denote the mean life expectancy in countries 1 and 2,respectively.Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.

A new study has found that,on average,6- to 12-year-old children are spending less time on household chores today compared to 1981 levels.Suppose two samples representative of study's results report the following summary statistics for the two periods. Which of the following are the appropriate competing hypotheses?

A university wants to compare out-of-state applicants' mean SAT math scores (μ₁)to in-state applicants' mean SAT math scores (μ₂).The university looks at 35 in-state applicants and 35 out-of-state applicants.The mean SAT math score for in-state applicants was 540,with a standard deviation of 20.The mean SAT math score for out-of-state applicants was 555,with a standard deviation of 25.It is reasonable to assume the corresponding population standard deviations are equal.At the 5% significance level,can the university conclude that the mean SAT math score for in-state students and out-of-state students differ?

A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males.Suppose 250 females and 200 males responded to the study.Which of the following is the correct conclusion for the test at ?

A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights.The magazine surveyed Standard Air (population 1)and Down Under airlines (population 2).Standard Air lost 45 out of 600 bags.Down Under airlines lost 30 of 500 bags.Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the correct value of the test statistic?