Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical wo rkday for people working in New York City who wear such trackers. A random sample of 71 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 10,797 steps and the standard deviation was 2,513 steps.
(a) Construct and interpret a 90 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
(b) A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 10,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation? Explain your answer