Exam 10: Statistical Inference Concerning Two Populations

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.Which of the following is the appropriate decision given a 5% level of significance?

What type of data is required to compare prices of the same textbooks sold by two different vendors?

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.Calculate a 95% confidence interval for the differenceμ₁ - μ₂.

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 mean of the difference calculated as pretest score minus posttest score. Which of the following are the appropriate hypotheses to determine if the training increases scores?

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 appropriate p-value?

For a statistical inference regarding ,it is imperative that the sampling distribution of is normally distributed.

A sports commentator believes that a particular basketball player is just awful in road games but relatively effective at home.To test this claim,the commentator takes a random sample of 36 road games and 49 home games and collects the player's scoring output in each game.He finds that in the 49 home games,the player averaged 12.3 points and his scoring output had a standard deviation of 2.6 points.Alternatively,in the 36 road games,the player averaged 8.9 points with a standard deviation of 5.6 points. a.Specify the competing hypotheses to determine if the player has a higher scoring average in home games. b.Calculate the value of the test statistic and the critical value at a 1% significance level.There is no reason to assume that the population variance of scoring output is equal for home and road games. c.Does the evidence support the commentator's claim at the 1% significance level?

What formula is used to calculate the degrees of freedom for the t test for comparing two population means when the population variances are unknown and unequal?

We always deal with matched-pairs sampling if two samples have the same number of observations.

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 hypotheses should be used to test the manager's claim?

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.What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?

A large city installed LED streetlights,in part,to help reduce crime in particular areas.The city collected the number of property crimes along nine randomly selected streets in the month before and after the LED light installation,and claims that crime has been reduced.The crime data is shown in the table. a.Specify the competing hypotheses to test the city's claim. b.Calculate the value of the relevant test statistic and find the critical value at the 5% significance level. c.Does the evidence support the city's claim at the 5% significance level?

Statistical inference about the differences between two population means based on _________ random samples.

Weather forecasters would like to report on temperatures in Washington,DC.In particular,they would like to compare the temperatures in December to temperatures in January to help potential tourists understand whether there is a difference.The average December temperature in a random sample of 16 days is 35 and the average January temperature in a random sample of 20 days is 33.The standard deviations based on historic information are 4 for December and 5 for January. a.Construct a 90% confidence interval for the difference between the population mean temperatures in December and January. b.Can we conclude with 90% confidence that the mean temperatures in December and January are different?

If the sampling distribution of cannot be assumed normal,we _________ .

According to a recent survey,women chat on their mobile phones more than men (CNN.com,August 25,2010).To determine if the same patterns also exist in colleges,Irina takes a random sample of 40 male students and 40 female students in her college.She finds that female students chatted for a sample average of 820 minutes per month,with a sample standard deviation of 160 minutes.Male students,on the other hand,chatted for a sample average of 760 minutes per month,with a sample standard deviation of 240 minutes.It is not reasonable to assume equal population variances. a.Specify the competing hypotheses to determine if female students chat,on average,more than male students. b.Calculate the value of the test statistic and its p-value.c.Make a conclusion at the 10% significance level.

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 is the appropriate conclusion at the 5% significance level?

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 is the correct value of the test statistic?

A farmer uses a lot of fertilizer to grow his crops.The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does.He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch.Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch.Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch,respectively.Assume the distribution of nitrogen in fertilizer is normally distributed.Let µ₁and µ₂ represent the average amount of nitrogen per batch for fertilizer's A and B,respectively.Which of the following is the correct value of the test statistic?

In August 2010,Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings.Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages.To test this claim,researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law.Of the 100 who fell behind just before the law was enacted,30 were able to avoid foreclosure,and of 144 who fell behind just after the law was enacted,48 were able to avoid foreclosure.Let p₁andp₂ represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted,respectively.Which of the following is the appropriate p-value to verify the claim?