# Central Limit Theorem - Confidence Level and Sample Size

#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.

_____________________

#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.