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

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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":
[1] The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.
[2] 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).
[3] The distribution of means will increasingly approximate a normal distribution as the size N of samples ...

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