Posted: February 5th, 2019
STAT-UB.0103 Homework Set 5
COMPLETE ANY 12 or more QUESTIONS FOR THIS HOMEWORK.1. Based on a sample of 50 x-values having mean 35.36 and standard deviation 4.26,(a)test at the 0.05 level of significance the null hypothesis H 0 : = 34 versusthe alternative H1 : 34.(b)find a 95% confidence interval for the population mean.(c)determine if the results to part (a) and (b) are mutually consistent.(d)use Minitab to give the p-value for the test in (a).2. The data set CHSNBA.MTP contains a number of variables for guards in theNational Basketball Association.(a)For the variable PPG, meaning points per game, test the null hypothesisH 0 : PPG = 11 against the alternative H1 : PPG 11 using the 0.05 levelof significance. The data file has n = 105, x = 10.70, s = 6.058.(b)Find a 95% confidence interval for PPG and reconcile your conclusion in(a) with this interval.3. Suppose that a sample of 200 accounts receivable entries at a large mail-orderbusiness had a mean price of $846.20 and a standard deviation of $1,840.80. Give a95% confidence interval for the population mean. Be sure to state any assumptions thatyou use.4. A sample of 612 voters were asked whether they would vote for candidate Wilson inthe upcoming election. Of these, 344 said that they intended to vote for Wilson. Is the344sample proportionstatistically significantly different from 0.50? Use the 5% level612of significance.5. The distributor of a certain variety of tomato seed has promised that 80% of the seedswill germinate under standard greenhouse conditions. You test this claim with 500seeds, and you find that 362 germinate successfully. At the 5% level of significance, testthe claim as H0: p = 0.80 against the alternative H1: p 0.80.7. Suppose that you are asked to test H0: 1 = 2 versus H1: 1 2 based on these data:Sample12n2723Average-0.0491-0.0307St.Dev.0.09900.0496Which form of the test would you use? What conclusion would you reach? The nextproblem asks for additional calculations with the same numbers.Page1STAT-UB.0103Homework Set 5((((((((((((((((((((((((((((((((((9. The weekly salaries of union electricians in two metropolitan areas were compared bytaking random samples of 50 in each area. The results were these:AreaN12Mean5050612.26659.65Standard deviation100.2083.73At the 5% level of significance, test the hypothesis H 0 : 1 = 2 versus the alternative H1: 1 = 2 .10. The management at Jackson & Flinch brokerage services has established dollarquotas for each of their brokers, but the brokers are generally not informed about thesequotas. As part of an experiment, 21 brokers (selected at random) were actually told theirannual dollar quotas just to see how knowledge of the quota would influence theirperformance. These brokers were compared with 15 others who were not told theirquotas. The data below indicate the fraction of annual quotas achieved by the end ofOctober:Told about quota?NMeanStandard deviationNo150.87100.0598Yes210.89240.0638At the 0.05 level of significance, test the null hypothesis H 0 : NO = YES against thealternative H1 : NO YES.15. Employees at McKenzie Corporation were given the opportunity to start 401-Kretirement plans beginning January 1, 2002, and 196 employees chose to do so. Of these,there were 94 who elected to sit through a three-hour seminar on making investmentdecisions. The dollar values of all these employees were noted on December 31, 2004,exactly two years later:Attend seminar?NoYesn10294Mean10,90011,500Standard deviation1,4403,570At the 0.05 level of significance, test the null hypothesis H 0 : NO = YES against thealternative H1 : NO < YES.FOR QUESTIONSPage2STAT-UB.0103Homework Set 5((((((((((((((((((((((((((((((((((17, CONVERT THE PROBLEM INTO A PROPORTION QUESTION BYCONSIDERING EITHER SUCCESS OR FAILURE, BUT NOT BOTH. USE ASIMILAR APPROACH FOR Q.1817. As part of an investigative process, a financial reporter has been comparing theadvice given by two investment newsletters. Each time a buy recommendation wasgiven, he noted the stock price; he then recorded whether the price was higher in exactlythree months. Each case in which the price was higher was called a success. Here isthe summary of his findings:NewsletterThird MilleniumGlobal StarshipSuccessFailure28441536Total numberof buyrecommendations4380Based on these values, does the reporter have an interesting story?18. People on marketing panels are often given products to use at home and evaluate. Inone panel, 75 people were given a one-gallon jug of Sunshine Cal-Plus Orange Juice totake home, and another 80 people were given a one-gallon jug of CitriSplash OrangeJuice to take home. When the panelists returned exactly one week later they were asked,Did you finish the gallon of orange juice? Here are the responses:Juice BrandSunshineCitriSplashTotalFinished Juice325486Did Not Finish Juice432669Total7580155At the 0.05 level of significance, is there a difference between these two juices for thisparticular question?
