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# Central Theorem, population shape, Tootsie Roll samples

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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?

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. (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 tests.
(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.)

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

Central Limit Theorem
The Central Limit Theorem shows the accuracy of the approximation larger improves as N ". The Central Limit Theorem predicts that regardless of the distribution of the "Parent population":
 The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.
 The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N).
 The distribution of means will increasingly approximate a normal distribution as the size N of samples ...

#### Solution Summary

Central theorem and population shape for Tootsie Roll samples are analyzed.

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