Question

in a random sample of 27 people, the mean commute time to work was 34.4 minutes and the standard deviation was 7.2 minutes. assume the population is normally distributed and use a t - distribution to construct a 98% 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 (31.0, 37.8) (round to one decimal place as needed.) the margin of error of μ is 3.4 (round to one decimal place as needed.) interpret the results. a. with 98% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval. b. if a large sample of people are taken approximately 98% of them will have commute times between the bounds of the confidence interval. c. with 98% confidence, it can be said that the commute time is between the bounds of the confidence interval. d. it can be said that 98% of people have a commute time between the bounds of the confidence interval.

Explanation:

A confidence interval for the population mean gives a range of values within which the true population mean is likely to lie. A 98% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, approximately 98% of those intervals would contain the true population mean. Option A correctly interprets this concept as it refers to the population mean. Option B is incorrect because it refers to a large sample of people (individual commute times) rather than the population mean. Option C is incorrect as it refers to "the commute time" (singular, likely an individual's time) instead of the population mean. Option D is wrong as it refers to 98% of people (individuals) having commute times in the interval, not the population mean.

Answer:

A. With 98% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.