#### MS 150 Statistics Spring 2004 Quiz Ten: 9.4

Eight students in PE 101j Joggling spring 2003 were asked to strongly disagree, disagree, agree, or strongly agree to the following statement, "I enjoyed participating in the physical activities of this class." The five responses were assigned numberical weights as seen below:

Strongly disagree: -2 | Disagree: -1 | Maybe: 0 | Agree: 1 | Strongly agree: 2

The eight answers from spring 2003 were 1, 1, 2, 1, 2, 2, 2, 2.
Use these eight spring 2003 answers to calculate the population values in your hypothesis test. This spring, spring 2004, the students were asked the same question again. This spring the average was 1.40. At an alpha of 0.10, is the spring 2004 average statistically significantly different than the spring 2003 average? Use a two-tailed test.

1. _________ Find the sample size for the spring 2003 data.
2. _________ Find the mean for the spring 2003 data, use this as the population mean.
3. _________ Find the standard deviation for the spring 2003 data.
4. Write out the null hypothesis:
5. Write out the alternate hypothesis:
6. _________ What is a?
7. _________ How many degrees of freedom are there?
8. _________ Determine tc
9. _________ Find the t-statistic t.
10. Make a sketch of the t-distribution including the tails, tc, and the t statistic here or on the back.
11. Do we:
1. ___ Reject the null hypotheis? OR
2. ___ Fail to reject the null hypothesis?

12. ___________________________ Is the spring 2004 average significantly different from the spring 2003 average at an alpha of 0.10?
13. _________Did the spring 2004 students experience less enjoyment in participating in the physical activities of the class than the spring 2003 students?
14. _________ What is the p-value for this hypothesis test?
15. _________ What is the largest possible confidence interval for which this difference is significant?
Statistic or Parameter Symbol Equations Excel
Hypothesis Testing
Degrees of freedom df = n-1 =COUNT(data)-1
Calculate a t-statistic (t) t (x - µ)/(sx/sqrt(n))
Calculate t-critical for a two-tailed test tc =TINV(a,df)
Calculate a p-value from a t-statistic t p = TDIST(ABS(t),df,#tails)