PR Newswire reported that in 2015, the mean number of text messages sent by Americans was 32 (source: “No time to talk: Americans sending/receiving five times as many texts compared to phone calls each day, according to new report,” www.prnewswire.com, Mar. 25, 2015). A major cell phone service provider conducted a study of a random sample of 400 customers in the age group between 18 and 35. The objective of the survey was to estimate the average number of text messages sent per day. The 400 people in the study sent 10,320 text messages on the day the study was conducted. The standard deviation in the number of texts sent per day by the people in this study was 9.5 messages.
a. What is the point estimate for the mean number of text messages sent per day by customers in this age group?
b. Calculate and interpret the 95% confidence interval estimate for the mean number of text messages sent per day by customers in this age group.

c. If the company would like to have a smaller margin of error, indicate what options are available.

d. Based on the result in part b, what conclusion might you reach about the PR Newswire statement about the mean being 32 messages per person?