Question

(Question 17, Question 18 and Question 19)  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 isn’t working, the commute distance is defined to be 0.) The correction factor for the standard error equals 1.

17. The standard error of the sample average commuting distance is,

1. 8.7
2. 9.0
3. .28
4. .56
5. None of the above

18. If possible, find a 95% confidence interval for the average commute distance of all heads of households in the town. If this isn’t possible choose response (e).

1. 8.7 plus or minus 2
2. 8.7 plus of minus .28
3. 8.7 plus or minus .56
4. 8.7 plus or minus .84
5. Not possible

19. If possible, find a 99.7% confidence interval for the average commute distance of all heads of households in the town. If this isn’t possible choose response (e).

1. 8.7 plus or minus 2
2. 8.7 plus of minus .28
3. 8.7 plus or minus .56
4. 8.7 plus or minus .84
5. Not possible

Answer 1

Given that, sample size (n) = 1000, sample mean = 8.7 miles

and standard deviation (s) = 9.0 miles

Q.17) The standard error of the sample average computing distance is,

Answer : 0.28

Q.18) Approximately 95% of the data values fall within 2 standard deviations of the mean.

Therefore, the 95% confidence interval for the average distance of all heads of households in the town is,

8.7 ± (2 * 0.28)

=> 8.7 ± 0.56

Q.19) Approximately 99.7% of the data values fall within 3 standard deviations of the mean.

Therefore, the 99.7% confidence interval for the average distance of all heads of households in the town is,

8.7 ± (3 * 0.28)

=> 8.7 ± 0.84