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# RESEARCH AND EVALUATION: Applied Statistics in Business

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Question 5
State the main points of the Central Limit Theorem for a mean.

Question 6
Why is population shape of concern when estimating a mean? What does sample size have to do with it?

8.46
A random sample of 10 Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were

3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477

(a)Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of =0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel).

8.62
In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1, 143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug test. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no.11 [November 1993], p. 31.]