Question

the confidence interval for the population mean μ is (32.5, 37) (round to one decimal place as needed) the margin of error of μ is 2.2 (round to one decimal place as needed) interpret the results. a. it can be said that 80% of people have a commute time between the bounds of the confidence interval. b. with 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval. c. with 80% confidence, it can be said that the commute time is between the bounds of the confidence interval. d. if a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval

Explanation:

To interpret a confidence interval, we use the concept that a confidence interval for a population mean (μ) gives a range of values within which we are confident (at the given confidence level) that the true population mean lies.

• Option A is incorrect because a confidence interval does not tell us about the proportion of people (individuals) with a certain commute time; it's about the population mean.
• Option B is correct. An 80% confidence interval for the population mean commute time means that if we were to construct many such intervals, about 80% of them would contain the true population mean. So, with 80% confidence, we can say the population mean commute time is between the bounds of the interval.
• Option C is incorrect because the confidence interval is about the population mean, not an individual's commute time.
• Option D is incorrect because the confidence interval is not about the proportion of the sample with commute times in the interval; it's about the population mean.

Answer:

B. With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.