Eric R. DodgePage 110/08/2018
ECO 157
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 (ESPN.com December 10-12, 2000).
Winner /Score
Minnesota / 96Phoenix / 86
San Antonio / 91
Houston / 82
Clippers / 92
Boston / 104
Dallas / 99
Sacramento / 101
Portland / 114
Utah / 125
b. Use the Empirical Rule to determine a range of winning scores that should be considered outliers. 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. (10 points)
2. What are the differences between qualitative and quantitative variables? (8 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. (14 points)
4. Describe a scenario where using the median might be more appropriate than using a mean to describe the central tendency of a sample of data. What does the 90th percentile represent as a measure of location? (10 points)
5. Using probabilities and your intuition, explain the difference between mutually exclusive events and independent events. (16 points)
6. During Spring break, 900 college students travel to Panama City, FL for a week of beachcombing and quiet reflection. 805 of these college students plan to drink beer while they are on vacation and the remaining 95 don’t drink beer at all. 340 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? If a student is selected randomly from the group of non-smokers, what is the probability that he/she is also a non-drinker? Are the events “beer drinker” and “smoker” independent events? Are they mutually exclusive events? Explain. (18 points)
7. 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? (6 points)
b. Develop and interpret 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)
8. 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 (at 95% confidence) that on average this pub was serving glasses of beer with less than 20 ounces? Explain your results to a journalist who didn’t complete an excellent statistics course. (20 points)
9. Samples of final examination scores for two statistics classes with different instructors provided the following results.
Instructor A / Instructor Bn1 = 18 / n2 = 15
= 72 / = 78
s1 = 8.5 / s2 = 10
With =.05, test whether these data are sufficient to conclude that the mean grades for the two classes differ. (15 points)
10. 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.
First calculate the missing t-statistics (3 points).
Thoroughly comment upon, interpret, and explain these results. (25 points)
SUMMARY OUTPUTRegression 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 / 3.28664E-08Income
($1000s) / 33.13300915 / 3.967905842 / 7.68206E-11
Household Size / 356.2959015 / 33.20089044 / 3.12342E-14
Final Exam, Fall 2000