Question:

A real estate office wants to make a survey in a certain town, which has 50,000 households, to determine how far the head of household has to commute to work. A simple random sample of 1,000 households are chosen.

1. It is found that on average, the heads of the sample households commuted 8.7 miles to work; the SD of the distances was 9.0 miles. (All distances are one-way; if someone isn’t working, the commute distance is defined to be 0.) If possible, find a 90%-confidence interval for the average commute distance of all heads of households in the town; if not, explain why.
2. In 721 of the sample households, the head of the household commuted by car. If possible, find a 90% confidence interval for the percentage of all households in the town where the head of the household commutes by car; if not, explain why.

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