Do students perform the same when they take an exam alone as when they take an exam in a classroom setting? Eight students were given two tests of equal difficulty. They took one test in a solitary room and they took the other in a room filled with other students. The results are shown below.

Alone	78	75	78	74	84	87	81	81
Classroom	69	69	80	75	73	80	76	74

Assume a Normal distribution. What can be concluded at the the = 0.01 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 t-test for the difference between two independent population means z-test for a population proportion

1. The null and alternative hypotheses would be:

H0:H0: Select an answer 1 p1 d Select an answer = < > Select an answer p2 2 0 (please enter a decimal)

H1:H1: Select an answer d 1 p1 Select an answer = > < Select an answer 0 2 p2 (Please enter a decimal)

1. The test statistic ? z t = (please show your answer to 3 decimal places.)
2. The p-value = (Please show your answer to 4 decimal places.)
3. The p-value is ? >
4. Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
5. Thus, the final conclusion is that ...
   • The results are statistically insignificant at = 0.01, so there is statistically significant evidence to conclude that the population mean test score taking the exam alone is equal to the population mean test score taking the exam in a classroom setting.
   • The results are statistically insignificant at = 0.01, so there is insufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting.
   • The results are statistically significant at = 0.01, so there is sufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting.
   • The results are statistically significant at = 0.01, so there is sufficient evidence to conclude that the eight students scored the same on average taking the exam alone compared to the classroom setting.