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Empirical Exercises 461

11.10 (Requires Section 11.3 and calculus) Suppose that a random variable Y has
the following probability distribution: Pr(Y = 1) = p, Pr(Y = 2) = q,
and Pr(Y = 3) = 1 - p - q. A random sample of size n is drawn from
this distribution, and the random variables are denoted Y1, Y2, c, Yn.

a. Derive the likelihood function for the parameters p and q.
b. Derive formulas for the MLE of p and q.

11.11 (Refer to Appendix 11.3) Which model would you use for:

a. A study explaining the number of hours spent by a person working
for income during a week.

b. A study explaining the level of satisfaction a person has with their job
(on a scale of 0 to 5).

c. A study of a consumer’s choice of mode of transport between bus,
car, and bicycle.

d. A study of the number of rainy days in a week.

Empirical Exercises

(Only two empirical exercises for this chapter are given in the text, but you can
find more on the text website, www.pearsonglobaleditions.com/Stock_Watson.)

E11.1 In April 2008 the unemployment rate in the United States stood at 5.0%.
By April 2009 it had increased to 9.0%, and it had increased further, to
10.0%, by October 2009. Were some groups of workers more likely to
lose their jobs than others during the Great Recession? For example, were
young workers more likely to lose their jobs than middle-aged workers?
What about workers with a college degree versus those without a degree,
or women versus men? On the textbook website, www.pearsonglobaleditions
.com/Stock_Watson, you will find the data file Employment_08_09, which
contains a random sample of 5440 workers who were surveyed in April
2008 and reported that they were employed full time. A detailed descrip-
tion is given in Employment_08_09_Description, available on the website.
These workers were surveyed one year later, in April 2009, and asked
about their employment status (employed, unemployed, or out of the labor
force). The data set also includes various demographic measures for each
individual. Use these data to answer the following questions.

a. What fraction of workers in the sample were employed in April
2009? Use your answer to compute a 95% confidence interval for