Question

in a random sample of five people, the mean driving distance to work was 19.1 miles and the standard deviation was 7.5 miles. assume the population is normally distributed and use the t - distribution to find the margin of error and construct a 95% confidence interval for the population mean μ. interpret the results.
(9.8, 28.4)
(round to one decimal place as needed.)
interpret the results. select the correct choice below and fill in the answer box to complete your choice.
(type an integer or a decimal. do not round.)
○ a. with % confidence, it can be said that the population mean driving distance to work (miles) is between the intervals endpoints.
○ b. with % confidence, it can be said that most driving distances to work (in miles) in the population are between the intervals endpoints.
○ c. % of all random samples of five people from the population will have a mean driving distance to work (in miles) that is between the intervals endpoints.
○ d. it can be said that % of the population has a driving distance to work (in miles) that is between the intervals endpoints.

Explanation:

A confidence interval gives an estimated range for the population mean. A 95% confidence interval means that if we were to take many samples and construct confidence intervals, about 95% of them would contain the true population mean. Option A correctly interprets this as being 95% confident that the population mean is within the interval. Options B and D refer to population values (not the mean), and option C misinterprets the confidence level as applying to sample means rather than the population mean.

Answer:

A. With 95% confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints.