Now let's see how sample size affects confidence intervals. We'll use the same data (first for n = 25 then n = 250) but instead of running a hypothesis test we'll construct confidence intervals.

a)Suppose the DoT sampled 25 commuters and found the average travel time for this sample of commuters was 25.6 minutes with standard deviation 7.8 minutes. Construct a 95% confidence interval for the new average commute time, then give two interpretations of this interval.

b)Now suppose the DoT sampled 250 commuters and found the average travel time for this sample of commuters was 25.6 minutes with standard deviation 7.8 minutes. Construct a 95% confidence interval for the new average commute time, then give two interpretations of this interval.

c)Explain how your confidence intervals in (g) and (h) differ. What causes this difference? Explain why large sample sizes do NOT cause misleading confidence intervals. (You saw above that large sample sizes could possibly lead to statistical significance without actual practical significance.)