Question

Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 transactions at random, she found that the average amount spent was $35.25. She then computed a 95% confidence interval to be between $31.84 and $38.66. Which statement gives a valid interpretation of the interval?

A. The store manager is 95% confident that the average amount spent by the 36 sampled customers is between S31.84 and $38.66.

B. There is a 95% chance that the mean amount spent by all customers is between $31.84 and $38.66.

C. There is a 95% chance that a randomly selected customer will spend between $31.84 and $38.66.

D. The store manager is 95% confident that the average amount spent by all customers is between $31.84 and S3866

Answer 1

D. The store manager is 95% confident that the average amount spent by all customers is between $31.84 and S3866

Step-by-step explanation:

A 95% confidence interval built based on a sample means that one can be 95% certain that the populational mean lies within the confidence interval found.

Options A and C can be readily discarded since they refer to the sample customers or a randomly selected customer and not the total customer population.

Option B is also incorrect because confidence intervals do not define the likelihood of a event happening.

Option D is correct because it assumes that the populational mean is, with a 95% confidence, within the interval.