a)

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a). 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 1000 households is chosen, the occupants are interviewed, and 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 doesn't work, the commute distance is defined to be 0. The 95% confidence interval for the average commute distance of all heads of households in the town is 8.7 miles +/- X miles. What is X?

B. The interviews included all individuals age 16+ in the 1,000 sample households. There were 2,500 such persons interviewed. On average, these 2,500 people commuted 7.1 miles to work and the SD of the distances was 10.2 miles. Which of the following statements is true? The confidence interval for the average commute distance for all individuals 16+ is 10.2 miles +/- 0.4 miles OR A confidence interval cannot be computed based on the information given because this was a simple random sample of households, but a cluster sample of people (where the cluster is the household). Our formula for the SE of an average only applies to simple random samples.

C. From the interviews, we find that in 721 of the sample households, the head of the household commuted by car. The 95% confidence interval for the percentage of all households in the town where the head of the household commutes by car is 72.1% +/- X%. What is X?