Question

in a random sample of 17 people, the mean commute time to work was 32.2 minutes and the standard deviation was 7.3 minutes. assume the population is normally distributed and use a t - distribution to construct a 99% confidence interval for the population mean μ. what is the margin of error of μ? interpret the results.
the confidence interval for the population mean μ is (27.0, 37.4).
(round to one decimal place as needed.)
the margin of error of μ is 5.2
(round to one decimal place as needed.)
interpret the results
a. it can be said that 99% of people have a commute time between the bounds of the confidence interval.
b. with 99% confidence, it can be said that the commute time is between the bounds of the confidence interval.
c. if a large sample of people are taken approximately 99% of them will have commute times between the bounds of the confidence interval.
d. with 99% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Explanation:

A confidence interval for the population mean gives a range of values within which the population mean is likely to lie. The interpretation of a confidence interval for the population mean \(\mu\) is about the population mean, not about individual data points or a large - sample proportion of data points.

Option A is incorrect because the confidence interval is about the population mean, not about 99% of people. Option B is incorrect as it doesn't specify that it's about the population mean. Option C is incorrect as it refers to a proportion of people in a large sample, while the confidence interval is about the population mean. Option D is correct as it correctly states that with 99% confidence, the population mean commute time is between the bounds of the confidence interval.

Answer:

D. With 99% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.