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Chapter 6: Q1E (page 338)
Findfor each of the following:
a.= .10
b.= .01
c.= .05
d.= .20
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鈥淥ut of control鈥� production processes. When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is 鈥渋n control鈥� during the period of time in which each sample is selected. (We cover quality-control charts in Chapter 13.) Suppose a concrete-block manufacturer samples nine blocks per hour and tests the breaking strength of each. During 1 hour鈥檚 test, the mean and standard deviation are 985.6 pounds per square inch (psi) and 22.9 psi, respectively. The process is to be considered 鈥渙ut of control鈥� if the true mean strength differs from 1,000 psi. The manufacturer wants to be reasonably certain that the process is really out of control before shutting down the process and trying to determine the problem. What is your recommendation?
Findfrom Table IV, Appendix D, for each of the following:
a. n = 10, = .05
b. n = 20, = .05
c. n = 50, = .01
Suppose you wish to estimate the mean of a normal population
using a 95% confidence interval, and you know from prior information that
a. To see the effect of the sample size on the width of the confidence interval, calculate the width of the confidence interval for n= 16, 25, 49, 100, and 400.
b. Plot the width as a function of sample size non graph paper. Connect the points by a smooth curve and note how the width decreases as nincreases.
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?
Suppose you want to estimate a population proportion,,and,,and.Find an approximate 95% confidence interval for.
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