The Residential Energy Consumption Survey found in 2001 that 47% of American hou

Question

The Residential Energy Consumption Survey found in 2001 that 47% of American households had internet access A market survey organizaiton repeated this study in a certain town with 25,000 households, using a simple random sample of 500 households: 239 of the sample households had internet access.
a) The percentage of households in the town with internet access is estimated as BLANK; this estimate is likely to be off by BLANK or so.
b)If possible, find a 95%-confidence interval for the percentage of all 25,000 households with internet access. If it's not possible explain why not.

Explanation / Answer

You need to know the radom sample size to do part a and b. n = 500 (missing data) x = 239 Sample proportion = p = x/n = 239/500 = 0.478 a) Percentage with internet acess = 239/500 * 100 = 47.8% The fraction in the other sample is 100-47.8 = 52.2% Standard deviation = v1st's fraction x 2nd fraction = v(0.478*0.522) = 0.4995 SE for number of people with internet access = vnumber of household * Standard deviation =v500 * .4995 = 11.17 To get percent that it is likely off by = 11.17/500*47 = 1.04% b) The 95% confidence interval for all percentage of all 25000 household is +/- 2 standard deviation = (47.8% +/- 2*1.04%) = (45.72,49.88%)

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