An April 2004 article on HearTheIssues.com stated that Americans watch an averag

Question

An April 2004 article on HearTheIssues.com stated that Americans watch an average of 3.7 hours of television per person per day. If the standard deviation for the number of hours of television watched per day is 3.9 and a random sample of 252 Americans is selected, the mean of this sample belongs to a sampling distribution.

(a) What is the shape of this sampling distribution?

(b) What is the mean of this sampling distribution? (Give your answer correct to one decimal place.)

(c) What is the standard deviation of this sampling distribution? (Give your answer correct to two decimal places.)

Explanation / Answer

a. Here n=252 which is sufficient large so as per central limit theorem distribution of mean is normally distributed.

b. As per central limit theorem mean is normally distributed with mean =xbar=3.7

c. As per central limit theorem mean is normally distributed with standard deviation = SE=standard deviation/sqrt(n)=0.25

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