Question

a study was done to estimate the mean commute time for a population of employed adults. a random sample of 25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was calculated to be $34.42 \pm 8.14$ minutes. a councilman is advocating for road repairs and states that, in this city, people with jobs commute an average of 45 minutes to work each day. does the confidence interval justify the councilmans statement?
no, because 45 minutes is greater than the upper bound of the confidence interval.
yes, because 45 minutes is greater than the upper bound of the confidence interval.
no, because the mean commute time from the 25 sampled adults was 34.42 minutes.
yes, because there were almost certainly some people in the sample of 25 adults whose commute was greater than 45 minutes.

Explanation:

Step1: Calculate interval bounds

Lower bound: $34.42 - 8.14 = 26.28$
Upper bound: $34.42 + 8.14 = 42.56$

Step2: Compare 45 to interval

45 > 42.56 (upper bound)

Step3: Evaluate councilman's claim

Since 45 is outside the interval, the claim is not justified.

Answer:

No, because 45 minutes is greater than the upper bound of the confidence interval.