A radio station is interested in whether listening habits differ by age. The station identified a random sample of 30 listeners aged 25 and younger, and asked them to keep track of the number of minutes they listened to the station in a week. The station also identified a random sample of 35 listeners who were over 25 years of age, and asked them to record their listening times. The data from the younger listeners yielded an average of 256.8 minutes, with a standard deviation of 50.3 minutes. The data from the older listeners yielded an average of 218.3 minutes, with a standard deviation of 92.4 minutes. At the 5% significance level, is there evidence of a difference in listening times between the two age groups?
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