Question

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. A 95% confidence interval is constructed for the population mean revenue. If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been _____________________.

Multiple Choice

wider, with a larger probability of reporting an incorrect interval

wider, with the same probability of reporting an incorrect interval

narrower, with a larger probability of reporting an incorrect interval

narrower, with the same probability of reporting an incorrect interval

Answer 1

narrower, with the same probability of reporting an incorrect interval

Explanation:

For the given scenario, we increase the sample from 25 to 40, so the margin of error will be decrease and therefore the confidence interval will be narrower. The width of the confidence interval decreases as we increase the sample size by assuming all other factors constant. The probability of reporting an incorrect interval will remain same for the both intervals, because we assume all other factors constant.