Question

Do college students enjoy playing sports less 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.

Playing Vs. Watching Sports

Play	6	2	4	7	5	10	5	1	7	9
Watch	5	3	6	6	6	10	7	2	6	10

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?

For this study, we should use Select an answer: t-test for a population mean, z-test for the difference between two population proportions, t-test for the difference between two dependent population means, z-test for a population proportion, t-test for the difference between two independent population means

1. The null and alternative hypotheses would be:     

H0: Select an answer p1 μd μ1 Select an answer < > = ≠ Select an answer μ2 p2 0 (please enter a decimal)   

H1: Select an answer μd p1 μ1 Select an answer < > ≠ = Select an answer μ2 0 p2 (Please enter a decimal)

2. The test statistic ? t or z  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? > or ≤ αα
5. Based on this, we should Select an answer: accept, fail to reject, reject the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean rating for playing sports is less than the population mean rating for watching sports.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is less than the population mean rating for watching sports.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports lower than watching sports on average.

Answer 1