Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores:

Grades
83.2
74.4
88
83.2
61.9
66.5
88
63.9
61.9
83.2

Test grades are believed to be normally distributed.

Use a significance level of $\displaystyle \alpha={5}\%$. ($\displaystyle {t}_{{\alpha}}={t}_{{0.05}}={1.8331}$)

1. State the alternative hypothesis: $\displaystyle {H}_{{A}}:$
   • $\displaystyle \mu\ne{65}$
   • $\displaystyle \mu>{65}$
   • $\displaystyle \mu<{65}$
2. State the mean of the sample:
3. State the standard error of the sample means:
4. State the test statistic: $\displaystyle {t}=$
5. State the p-value:
6. Decision:
   • Reject the null hypothesis.
   • Fail to reject the null hypothesis.
7. Conclusion:
   • We do not have sufficient evidence to conclude that the mean GPA of night students is higher than 65.
   • We have sufficient evidence to conclude that the mean GPA of night students is higher than 65.
8. Hopefully you drew a picture of all of this. ☺