Question 8.73

commutedist

73. Commuting Distances. A university is trying to attract more commuting students from the local community. As part of the research into the modes of transportation students use to commute to the university, a survey was conducted asking how far commuting students commuted from home to school each day. A random sample of 30 students provided the distances (in miles) shown in the table below. Assume that the standard deviation is miles.

14 10 14 12 12 11 5 6 9 14 9 9 4 7 15
9 7 7 12 10 15 10 6 11 9 11 10 11 7 12
  1. Compute and interpret the margin of error for a confidence interval with 95% confidence.
  2. Construct and interpret a 95% confidence interval for the population mean commuting distance.

8.1.73

(a) miles. We can estimate μ, the mean commuting distance, to within 1.07 miles with 95% confidence. (b) (8.86, 11.00). We are 95% confident that the true mean commuting distance lies between 8.86 miles and 11.00 miles.