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Chapter 6: Q110SE (page 330)
Calculate the finite population correction factor for each
of the following situations:
a. n = 50, N = 2,000
b. n = 20, N = 100
c. n = 300, N = 1,500
a.0.9876
b. 0.8989
c. 0.8947
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It costs you \(10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of \)1,500.
a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume.
b. If you used a 90% confidence level, would your answer to part a change? Explain.
Largest private companies. IPOs鈥攊nitial public offerings of stock鈥攃reate billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 216 Largest Private Companies list are given in the table below
a. Describe the population from which the random sample was drawn.
b. Use a 98% confidence interval to estimate the mean revenue of the population of companies in question
c. Interpret your confidence interval in the context of the problem
d. What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b?
e. Suppose Forbes reports that the true mean revenue of the 216 companies on the list is $5.0 billion. Is the claim believable?
College dropout study. Refer to the American Economic Review (December 2008) study of college dropouts, Exercise 2.79 (p. 111). Recall that one factor thought to influence the college dropout decision was expected GPA for a student who studied 3 hours per day. In a representative sample of 307 college students who studied 3 hours per day, the mean GPA was and the standard deviation was . Of interest is, the true mean GPA of all college students who study 3 hours per day.
a. Give a point estimate for .
b. Give an interval estimate for . Use a confidence coefficient of .98.
c. Comment on the validity of the following statement: 鈥�98% of the time, the true mean GPA will fall in the interval computed in part b.鈥�
d. It is unlikely that the GPA values for college students who study 3 hours per day are normally distributed. In fact, it is likely that the GPA distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval?
Findfor each of the following:
a.= .10
b.= .01
c.= .05
d.= .20
Explain the difference between an interval estimator and a point estimator for
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