Final Exam, Winter 2002

Eric R. Dodge Page 1 1/9/2018 ECO 157 0fce4360736ea334f789c9a066af72cd.doc Name: FINAL EXAM Use only the space provided to answer the following questions. Whenever possible, show your work for potential partial credit. You may use the back of page 5 for additional space. NOTE: When performing numerical calculations, keep at least 4 decimals. (i.e., do NOT round .2265 to .227 or .23) 1. A sample of 10 National Basketball Association (NBA) scores provided the following winning teams and the number of points scored (The Cincinnati Enquirer, January 5, 1998). Winner Score Indiana 89 a. Compute and interpret the mean, median, mode and standard deviation for Cleveland 95 the data. (20 points) Chicago 105 Portland 97 Boston 106 San Antonio 84 New York 88 Minnesota 109 Utah 97 L.A. Clippers 97

b. In another game, Seattle beat Vancouver 120 to 108. How would the Empirical Rule be used to determine whether the Seattle score should be considered an outlier? Is the Seattle score an outlier? Explain. (15 points)

c. Assume that the distribution of points scored by winning teams is normal. Estimate the percentage of all NBA games in which the winning team will score 105 or more points. Estimate the percentage of games in which the winning team will score 80 or fewer points. (5 points)

0fce4360736ea334f789c9a066af72cd.doc Eric R. Dodge Page 2 1/9/2018 ECO 157 0fce4360736ea334f789c9a066af72cd.doc 2. What are the differences between qualitative and quantitative variables? Give an example of each. (10 points)

3. In a sample of 20 adult men, data were collected on their height (measured in inches above 5’ tall) and weight (in pounds). Some descriptive statistics are given below. The covariance between height and weight is 31.0632. Interpret this covariance. In addition, calculate the correlation coefficient and interpret it as well. (20 points) HEIGHT (" OVER 5 FT) WEIGHT

Mean 10.35 Mean 169.4 Median 10 Median 165 Mode 9 Mode 165 Standard Deviation 2.207046133 Standard Deviation 16.32692 Range 10 Range 65 Minimum 5 Minimum 140 Maximum 15 Maximum 205 Count 20 Count 20

4. Using probabilities and your intuition, explain the difference between mutually exclusive events and independent events. (20 points)

0fce4360736ea334f789c9a066af72cd.doc Eric R. Dodge Page 3 1/9/2018 ECO 157 0fce4360736ea334f789c9a066af72cd.doc 5. During Spring break, 900 college students travel to Panama City, FL for a week of beachcombing and quiet reflection. 810 of these college students plan to drink beer while they are on vacation and the remaining 90 don’t drink beer at all. 640 students also smoke cigarettes, and all of the smokers are also beer drinkers. If a student is selected randomly, what is the probability that the student is a smoker, given that he/she is a beer drinker? Are the events “beer drinker” and “smoker” independent events? Are they mutually exclusive events? Explain. (20 points)

6. Although airline schedules and cost are important factors for business travelers when choosing an airline carrier, a USA Today survey found that business travelers list an airline’s frequent flyer program as the most important factor (USA Today, April 11, 1995). From a sample of n=1993 business travelers who responded to the survey, 618 listed a frequent-flyer program as the most important factor. a. What is the point estimate of the proportion of the population of business travelers who believe a frequent flyer program is the most important factor when choosing an airline carrier? (5 points)

b. Develop a 95% confidence interval estimate of the population proportion. (10 points)

c. How large a sample would be required to report the margin of error of .01 at 95% confidence? Would you recommend that USA Today attempt to provide this degree of precision? Why or why not? (10 points)

0fce4360736ea334f789c9a066af72cd.doc Eric R. Dodge Page 4 1/9/2018 ECO 157 0fce4360736ea334f789c9a066af72cd.doc 7. In 1994 in Great Britain there was hot debate over a regulation that required bigger beer glasses to accommodate a full 20-ounce British pint and a creamy head. Brewers and pub landlords would be fined for selling less. As a test, an agent visited a pub at ten random times, ordering a draft on each visit and found that the sample mean was 19.9389 ounces with a sample standard deviation of .1498 ounces. Would you conclude that on average this pub was serving glasses of beer with less than 20 ounces? Explain your results. (Test at the 5% level.) (20 points)

8. Samples of final examination scores for two statistics classes with different instructors provided the following results. Instructor Instructor B A n1 = 12 n2 = 15 x-bar1 = 72 x-bar2 = 78 s1 = 8 s2 = 10 With =.05, test whether these data are sufficient to conclude that the mean grades for the two classes differ. (20 points)

0fce4360736ea334f789c9a066af72cd.doc Eric R. Dodge Page 5 1/9/2018 ECO 157 0fce4360736ea334f789c9a066af72cd.doc 9. Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual household income (X1), household size (X2), and annual credit card charges (Y) for a sample of 50 consumers. Below are regression results that attempt to shed light on this empirical relationship. Thoroughly comment upon, interpret, and explain these results. (25 points) SUMMARY OUTPUT Regression Statistics Multiple R 0.908603921 R Square 0.825561086 Adjusted R Square 0.818138154 Standard Error 398.0910071 Observations 50 ANOVA df SS MS F Significance F Regression 2 35250755.67 17625377.84 111.2176468 1.50876E-18 Residual 47 7448393.148 158476.4499 Total 49 42699148.82 Coefficients Standard Error t Stat P-value Intercept 1304.904779 197.6548431 6.601936785 3.28664E-08 Income 33.13300915 3.967905842 8.350250854 7.68206E-11 ($1000s) Household Size 356.2959015 33.20089044 10.73151644 3.12342E-14

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