Winter 1998, Final Exam

Winter 1998 FINAL EXAM

Use only the space provided to answer the following questions. Whenever possible, show your work for potential partial credit. NOTE: When performing numerical calculations, keep at least 4 decimals. (i.e., do NOT round .2265 to .227 or .23)

1. Although it doesn’t get much economic attention, a small but growing list of economists are convinced that the per pound price of a head of iceberg lettuce should be considered a new economic indicator. Below is a table of average monthly ($) prices in U.S. cities for 1997.

Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1997	0.651	0.594	0.614	0.666	0.598	0.593	0.649	0.694	0.737	0.823	1.01	0.699

Calculate the mean, median, standard deviation and range of these lettuce prices. Why is it recommended to report both means and medians when describing data? (25 points)

2. Some would argue that strong demand in the lettuce market (a higher price) should reflect lower unemployment rates in the agricultural sector of the labor market. Others would contend that higher prices indicate short supply and thus higher unemployment. Below is a table of monthly unemployment rates (%) in this sector of the U.S. labor market in 1997.

Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1997	8.7	9	9.3	9.5	7.6	10.4	8.4	8.9	9	9.6	8.6	9.7

Calculate the mean, median, and standard deviation of these unemployment rates. (15 points)

Which of the above variables exhibits more volatility in 1997? Explain how you came to this determination. (15 points)
The covariance between 1997 lettuce prices and unemployment rates in the 1997 agricultural sector is equal to -.0046. Interpret this finding. Calculate the correlation coefficient between these two variables and interpret your result. Do your findings support the demand-side or the supply-side theories of how lettuce prices might affect agricultural unemployment rates? Explain. (20 points)

Using probabilities and your intuition, explain the difference between mutually exclusive events and independent events. (15 points)

During Spring break, 100 college students travel to Panama City, FL for a week of beachcombing and quiet reflection. 80 of these college students plan to drink beer while they are on vacation and 20 don’t drink beer at all. 40 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)

What important role does the Central Limit Theorem serve whenever a point estimator is used to estimate a population parameter? (20 points)

8. Before the hiring of an efficiency expert, the mean productivity of a firm’s employees was 45.4 units per hour, with a standard deviation of 4.5 units per hour. After incorporating the changes recommended by the expert, it was found that a sample of 30 workers produced a mean of 47.5 units per hour. Using the .01 level of significance, evaluate the efficiency expert’s original contention that his methods would "substantially increase" worker productivity. (15 points)

9. In a major industry where well over 100,000 manufacturing employees are represented by a single union, a simple random sample of n=100 union members finds that 57% of those in the sample intend to vote for the new labor contract negotiated by union and management representatives.

What is the 99% confidence interval for p, the population proportion of union-represented employees who intend to vote for the labor contract? What does this interval represent? (20 points)

Based on your response to (a), does contract approval by the union appear to be a "sure thing"? Why or why not? (15 points)

10. It is hypothesized that the number of housing starts (millions) is a significant determinant of the value of rug and carpeting shipments ($ billions). Below are regression results, derived from data over the six-year time period (1989-1994), that attempt to shed light on this empirical relationship. Thoroughly comment upon, interpret, and explain these results. (20 points)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.770563
R Square	0.593767
Adjusted R Square	0.492209
Standard Error	0.48585
Observations	6

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	4.660666	1.72815	2.69691	0.054268	-0.13746	9.45879	-0.13746	9.45879
Housing	3.30757	1.367912	2.417969	0.072923	-0.49037	7.105512	-0.49037	7.105512

LOWEST QUIZ REPLACEMENT QUESTION: (20 points)

If you respond to this question, I will grade it and replace your lowest quiz score with the score on this question. If you do not respond to this question, your lowest quiz score will stand and be included in the calculation of your final course grade.

An article titled "The Bloodbath In Market Research" in Business Week (February 11, 1991) stated that "the validity of surveys is being jeopardized by the growing refusal of Americans to participate. Annoyed by the intrusiveness, 36 percent of consumers declined to answer a phone query in 1990."

How does refusal to participate jeopardize the validity of surveys?

How could you test the correctness of the claim that 36 percent of Americans called would not respond to questions?

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