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Normal Distribution and Confidence Intervals

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

6. Why is population shape of concern when estimating a mean? What does sample size have to do with it?"
(Doane and Seward, p. 338)

Exercise 8.46

A random sample of 10 miniature 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.

Exercise 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 tests.

(b) Why is the normality assumption not a problem, despite the very small value of p?

Thank you