Questions: Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Assume a Normal distribution. What can be concluded at the α=0.05 level of significance?

Solution Steps

The mean for playing sports is (7+3+2+1+7+4+3+3+2+10)/10 = 4.2

The mean for watching sports is (4+5+1+1+8+2+1+2+3+8)/10 = 3.5

Null hypothesis: There is no difference between the population mean rating for playing sports and the population mean rating for watching sports.

Alternative hypothesis: The population mean rating for playing sports is greater than the population mean rating for watching sports.

Since the same ten students rate both playing and watching sports, a paired t-test is appropriate. Software or a calculator can be used to calculate the p-value. The p-value is 0.284.

Since the p-value (0.284) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.

Final Answer: The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.