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# Central Limit Theorem - Confidence Level and Sample Size

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#1
Answer the following based upon the implications of the Central Limit Theorem (assume sample size larger than 30 when samples are mentioned in (a) and (b) below).

a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

b) How does the standard deviation of the sampling distribution of all possible sample means from a population compare to the standard deviation of the population.

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#2
Suppose you want to estimate the percentage of all voters across the nation who voted for Obama in the Democratic party primaries and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 90% confidence level. What size sample is required? (assume that no estimate of p-hat is known)

https://brainmass.com/statistics/central-limit-theorem/central-limit-theorem-confidence-level-and-sample-size-173996

#### Solution Preview

(1) (a) As the sample size increases (and for sample size > 30) the mean of the sampling distribution of the means equals (or very closely approaches) the population mean.

(b) As ...

#### Solution Summary

Two questions on Central Limit Theorem - Confidence Level and Sample Size solved.

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## Finding Confidence Interval and Central Limit Theorem

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.

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 a95 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?

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

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

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