In assessing the value of radio advertisements, sponsors consider not only the total number of listeners but also their ages. The 18 to 34 age group is considered to spend the most money. To examine the issue, the manager of an FM station commissioned a survey. One objective was to measure the difference in listening habits between the 18 to 34 age and 35 to 50 age groups. The survey asked 250 people in each age category how much time they spent listening to FM radio per day. The results (in minutes) were recorded and stored in stacked format (column 1 = Age group and column 2 = Listening times).

a. Can we conclude that a difference exists between the two groups?

b. Estimate with 95% confidence the difference in mean time listening to FM radio between the two age groups.

c. Are the required conditions satisfied for the techniques you used in parts (a) and (b)?