Problems #5-Sample Size A. In 2010, the Census Bureau estimated the proportion o

Question

Problems #5-Sample Size A. In 2010, the Census Bureau estimated the proportion of all Americans who own their homes to be 0.669. An urban economist wants to estimate the current (2016) proportion of all Americans who own their homes i. Making use of the Census Bureau estimate as a starting point, what sample size does she need to be 90% confident AND have the estimate within 0.02 of the true proportion? SHOW YOUR WORK. If she ignores the Census Bureau estimate, what sample size does she need to be 90% confident AND have the estimate within 0.02 of the true proportion? SHOW YOUR WORK. ii. B. A researcher wants to estimate the mean hours per week that Americans spend watching television. He has read an article about a survey conducted in 2014 that had s = 7.5 hours per week spent watching television. What sample size does he need to estimate the population mean within 2 hours per week with 95% confidence? SHOW YOUR WORK.

Explanation / Answer

Z0.025*(0.22/n)1/2 = 0.02 => 1.64*(0.22/n)1/2 = 0.02

        Z0.01/2*(p*(1-p)/n)1/2 = 0.04 => 1.64*(p*(1-p)/n)1/2 = 0.02

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =6724*1/4 =1681

So if no estimate were available for the proportion we need 1681 sample size.

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