Seventy-seven students at the University of Virginia were asked to keep a diary of conversations with their mothers, recording any lies they told during these conversations (San Luis Obispo Telegram-Tribune, August 16, 1995). It was reported that the mean number of lies per conversation was 0.5. Suppose that the standard deviation (which was not reported) was 0.4.
a. Suppose that this group of 77 is a random sample from the population of students at this university. Construct a 95% confidence interval for the mean number of lies per conversation for this population.
b. The interval in Part (a) does not include 0. Does this imply that all students lie to their mothers? Explain.