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 narrower, with a larger probability of reporting an incorrect interval wider, with the same probability of reporting an incorrect interval narrower, with the same probability of reporting an incorrect interval wider, with a larger probability of reporting an incorrect interval Next

Answer 1

Narrower with the same probability of reporting an incorrect interval

Explanation:

Increasing the sample size shrinks the width of the confidence interval because the larger the sample size, the more accurate the sample represents the true population.

Standard Error is calculated by multiplying the z or t score of the confidence level by the standard deviation, then dividing by the square root of the sample size

E = z(s)/√n

t scores are used for samples below a size of 30. All t values for 95% confidence are higher than the z score of 1.96, which is used when the sample is greater than 30. This causes a larger value for the error estimate, therefore creating a larger width for the confidence interval.