Chapter 2 CQ1) Which variable is least likely to be regarded as ratio data? a. Length of time required for a randomly-chosen vehicle to cross a toll bridge (minutes). b. Weight of a randomly-chosen student (pounds). c. Number of fatalities in a randomly-chosen traffic disaster (persons). d. Student's rating of a professor's performance (Likert scale). Answer : D CQ2) Your rating of the food served at a local restaurant using a 3-point scale of 0 = gross, 1 = decent, 2 = yummy is ___________ data. a. nominal. b. ordinal. c. interval. d. ratio. Answer : B CQ) The mean and median of a certain variable, were given to be $25,000 and $31,000 respectively. What is the shape of the distribution? a. Left Skewed b. Symmetric c. Right Skewed d. Cannot be determined from the given information. Answer : A 1) Given P(A) = 0.5; P(B) = 0.4 and P(A and B) = 0.15. Applying the General law of Addition, what is P(A or B)? a) b) c) d) 0.15 0.2 0.7 0.75 2) Given P(A) = 0.6; P(B) = 0.4 and P(A and B) = 0.24. Are events A and B independent? a. Yes, they are independent b. No, they are not independent CQ1) Given P(A) = 0.5; P(B) = 0.7 and P(A and B) = 0.25. Are events A and B independent? a. Yes, they are independent b. No, they are not independent CQ2) What is the probability that a randomly chosen order was completed by Supplier 2? a) b) c) d) 0.2 0.4 0.6 0.64 Contingency table Supplier 1 Supplier 2 Total Defect No Defect Total 0.16 0.24 0.4 0.2 0.4 0.6 0.36 0.64 1 CQ3) Are defects independent of suppliers? a. Yes, they are independent b. No, they are not independent What do you think about the pace of this course? In your opinion, how are topics covered? a. Too fast b. Slightly fast c. Just right d. Slightly slow e. Too Slow CQ) To find out if its advertising works, a store surveyed some people and collected data on whether they saw the ad (saw ad, did not see ad), and whether a purchase was made (purchase, no purchase). Three joint probabilities were calculated as P(see ad and purchase) = 0.18 P(see ad and no purchase) = 0.42 P(do not see ad and purchase) = 0.12 Are the ads effective? In other words are seeing an ad and purchasing independent? a. b. c. d. Yes, they are independent No, they are not independent Not enough data My head hurts CQ1) Following is the distribution of the number of absent employees per day. X 0 1 2 3 4 5 6 7 P(x) .005 .025 .310 .340 .220 .080 .019 .001 What is P(2 < X < 5)? a) b) c) d) .340 .560 .870 .950 CQ2) What is the mean number of absent employees per day? a) b) c) d) 2.758 3.066 3.783 4.125 CQ1) : A small feeder airline knows that the probability is .10 that a reservation holder will not show up for its daily 7:15 am flight into a hub airport. The flight carries 9 passengers. If the airline overbooks by selling 10 seats, what is the probability that no one will have to be bumped? a) b) c) d) .349 .387 .612 .651 CQ) Most airline flights do not experience any mishandled bags. Some flights will have one bag lost; a few will have two bags lost; very rarely will a flight lose three bags, and so on. It is reasonable to assume that the average number of bags lost is 0.3 bags/flight and that the number of bags lost on a randomly selected flight follows a Poisson distribution. What is the probability that 2 or more bags are lost on a particular flight? A. 0.037 B. 0.7408 C. 0.2222 D. 0.9630 CQ1) Find P (-1.4 < Z < 0.6). a) b) c) d) 0.0808 0.6449 0.7257 0.8065 CQ2) Lifetimes of light bulbs manufactured by a certain company are normally distributed with a mean of 5100 hours and standard deviation of 200 hours. They are advertised to last for 5000 hours. What is the probability that a bulb lasts longer than the advertised figure? a) b) c) d) .3085 .6915 .7889 .9900 Approximately how many hours do the top 5% of all bulbs last? CQ1) If arrivals occur at a mean rate of 3.6 events per hour, the exponential probability of waiting less than 0.5 hours for the next arrival is a. .7122 b. .8105 c. .8347 d. .7809 CQ2) If arrivals occur at a mean rate of 2.6 events per minute, the exponential probability of waiting more than 1.5 minutes for the next arrival is a. .0202 b. .0122 c. .0535 d. .9795 Problem 7.77 from text) MBTF = 10,000 hours. What is the probability of failure within the first 10,000 hours? 1) If Z is such that the area under the curve between +z and –z is 0.50, what is the value of z? 2) Final marks in a statistics class are normally distributed with a mean of 70 and a standard deviation of 10. The professor must convert all marks to letter grades. He decides that he wants 10% A’s, 30% B’s, 40% C’s, 15% D’s and 5% F’s. Find the cutoffs for each letter grade. CQ1) The shape of the sampling distribution of the sample mean is a) b) c) d) Approximately normal for n>= 30 Skewed to the left Uniform Indeterminate CQ2) To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken. The mean is $850 and the standard deviation is $54. A 99% confidence interval for the population mean is a. $823.72 to $876.28 b. $832.36 to $867.64 c. $826.82 to $873.18 d. $825.48 to $874.52 CQ3) A recent poll of 900 voters on early voting (by Gallup) reported that 30% of all voters would vote early. Determine the 95% Confidence Interval. CQ1) A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice. What is the width of a 90% confidence interval for the proportion that plan to specialize in family practice? a. ±.0447 b. ±.0736 c. ±.0876 d. ±.0894 ANSWER: B CQ2) A financial institution wishes to estimate the mean balances owed by its credit card customers. The population standard deviation is estimated to be $300. If a 99 percent confidence interval is used and an interval of ± $75 is desired, how many cardholders should be sampled? a. 3382 b. 629 c. 87 d. 107 ANSWER: D CQ3) Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of ± 2% with 90% confidence. What is the necessary sample size, to be conservative? a. 4,148 b. 2,401 c. 1,692 d. 1,604 ANSWER: c Chapter 9 CQ1) The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: a. H o : 35 vs. H1 : 35 b. H o : 35 vs. H1 : 35 c. H o : X 35 vs. H1 : X 35 d. H o : X 35 vs. H1 : X 35 ANSWER: b CQ2) A spouse stated that the average amount of money spent on Christmas gifts for immediate family members is above $1200. The correct set of hypotheses is: a. H 0 : 200 vs. H1 : 1200 b. H 0 : 1200 vs. H1 : 1200 c. H 0 : 1200 vs. H1 : 1200 d. H 0 : 1200 vs. H1 : 1200 ANSWER: c Problem) Nike has introduced a new golf ball, endorsed by Tiger Woods, and claims that the new ball will travel further than Titleist golf balls. A low-handicap golfer who currently uses Titleist has observed that his average drive is 230 yards, with a (population) standard deviation of 10 yards. He hits 100 drives with the new Nike ball and measures the distances. The average distance was 231.56 yards. Using a significance of 1%, conduct a hypothesis test of Nike’s claim. Problem) A television commercial for a toothpaste claims that more than four out of five dentists recommend the product. A consumer protection group polls 400 dentists and finds that 329 dentists recommend the product. Can we infer whether the claim is true at 10% level of significance? Problem) USA Today reported recently that executives spend one hour reading and sending email. A statistician doubted the report and conducted a survey of his own. A random sample of 162 executives yielded a mean of 63.7 minutes with a sample standard deviation of 18.94 minutes. Test the alternative hypothesis that the mean is not one hour at a 5% significance level. CQ1) Researchers determined that 60 Kleenex tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: x = 52 and s = 22. Suppose the alternative we wanted to test was H1 : 60 . Which of the following is true? a. reject H o if t > 1.6604 b. reject H o if t < - 1.6604 c. reject H o if t > 1.9842 or Z < - 1.9842 d. reject H o if t < - 1.9842 Problem) A couriers claim that it takes less than 6 hours for delivery is being tested. A sample of 12 deliveries yielded the following delivery times, 3.03 6.33 6.50 5.22 3.56 6.76 7.98 4.82 Is there evidence at the 5% level, to support the courier’s claim? 7.96 4.54 5.09 6.46 NEW FORMULA: A Formula One Ferrari at a pit stop during the Chinese Grand Prix. In one of the more unlikely collaborations of modern medicine, Britain's largest children's hospital has revamped its patient handoff techniques by copying the choreographed pit stops of Italy's Formula One Ferrari racing team. The hospital project has been in place for two years and has already helped reduce the number of mishaps. Ferrari • A Hospital Races to Learn Lessons of Ferrari Pit Stop Page November 14, 2006 WSJ Suppose a hospital in the US has adopted these techniques. They’ve studied their surgical handoffs both before and after using the pit stop techniques. From a sample of 53 handoffs prior to changes they found there were 20 handoffs with technical errors. From a sample of 65 handoffs after the changes they found there were 18 handoffs with technical errors. Has the proportion of handoffs with technical errors decreased since the changes? Suppose the sample sizes were actually 530 and 650 and the sample proportions stayed the same. Which do you believe would be most likely? A) B) The p-value would drop significantly allowing us to reject the null hypothesis. There would be no change in the result of the hypothesis test. Consider this same hospital. In addition to tracking handoff errors, the hospital also tracks handoff time. In these same samples, the average handoff time before changes was 23 minutes with a standard deviation of 5 minutes. After the changes, the average handoff time was 15 minutes with a standard deviation of 8 minutes. Recall that the sample sizes were 53 and 65, respectively. Has there been a significant reduction in average handoff time? The manufacturer of an MP3 Player wanted to know whether a 10% reduction in price is enough to increase the sales of their product. To investigate, the owner randomly selected seven outlets and collected sales data from the month of February. For the month of March the MP3 player sold at the reduced price. Reported below are the number of units sold at each of the outlets for February and March. At the .10 level of significance, can the manufacturer conclude that the price reduction resulted in an increase in sales? Sales Feb 138 121 88 115 141 125 96 March 128 134 152 135 134 126 112 Random samples of Tuesday and Friday withdrawals from a college-campus ATM were compared to see whether or not there was a difference in the means. Friday: 82.40, 75.35,25 Tuesday: 41.00, 35.23, 20 CQ) A regression analysis between Mileage (dependent variable in miles per gallon) and Speed (independent variable in mph) yielded the least squares regression line ŷ 50.6563 – 0.3531x. What is the gas mileage of a car traveling at 70 mph. a. 25.94 b. 26.87 c. 31.25 d. 32.49 Chi-Square test of Independence Problem 1) Republicans Democrats Independent Against For Bailout Bailout 27 33 10 29 21 20 Problem 2) Close Gay Friend or Family Allowed to Marry Should Not be Allowed to marry No Close Gay Friend or Family 67 19 32 62 Chi-Square test for the goodness of fit A statistics professor posted the following grade distribution guidelines for his elementary statistics class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs. Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines.