Question

in a random sample of 20 people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.1 minutes. assume the population is normally distributed and use a t - distribution to construct a 90% 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 (28.0, 33.5).
(round to one decimal place as needed.)
the margin of error of μ is 2.8
(round to one decimal place as needed.)
interpret the results
○ a. it can be said that 90% of people have a commute time between the bounds of the confidence interval.
○ b. if a large sample of people are taken approximately 90% of them will have commute times between the bounds of the confidence interval.
○ c. with 90% confidence, it can be said that the commute time is between the bounds of the confidence interval.
○ d. with 90% 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 that with a certain level of confidence (in this case \(90\%\)), the population mean \(\mu\) is within the bounds of the confidence interval.
• Option A is incorrect because it refers to the proportion of people, not the population mean.
• Option B is incorrect as it also refers to a proportion of people in a sample, not the population mean.
• Option C is incorrect as it refers to the commute time (a single value for an individual), not the population mean.

Answer:

D. With 90% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.