Confidence interval mistakes and misunderstandings. Suppose that 101 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week.5 The sample mean x was found to be 4.2 hours, and the sample standard deviation was s = 2.5 hours
(a) Cary Oakey computes the 95% confidence interval for the average time on the site as 4.2 ± 1.984(2.5/101). What is his mistake?
(b) He corrects this mistake and then states that "95% of the members spend between 3.71 and 4.69 hours a week on the site." What is wrong with his interpretation of this interval?
(c) The margin of error is slightly less than half an hour. To reduce this to 15 minutes, Cary says that the sample size needs to be doubled to 202. What is wrong with this statement?