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

Exam Scores

Alone	96	76	73	71	85	87	75	86
Classroom	89	68	67	62	79	80	73	86

Assume a Normal distribution. What can be concluded at the theαα = 0.01 level of significance level of significance?

For this study, we should use Select an answerz-test for apopulation proportionz-test for the difference between twopopulation proportionst-test for the difference between twoindependent population meanst-test for a population meant-test forthe difference between two dependent population means

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answerμdμ1p1 ?=<>≠ Select ananswer0μ2p2 (please enter a decimal)   

H1:H1:  Select an answerp1μdμ1 ?=><≠ Select ananswer0μ2p2 (Please enter a decimal)

1. The test statistic ?tz = (please show your answer to 3 decimalplaces.)
2. The p-value = (Please show your answer to 4 decimalplaces.)
3. The p-value is ?≤> αα
4. Based on this, we should Select an answeracceptrejectfail toreject the null hypothesis.
5. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.01, sothere is statistically significant evidence to conclude that thepopulation mean test score taking the exam alone is equal to thepopulation mean test score taking the exam in a classroomsetting.
   • The results are statistically significant at αα = 0.01, sothere is sufficient evidence to conclude that the eight studentsscored the same on average taking the exam alone compared to theclassroom setting.
   • The results are statistically significant at αα = 0.01, sothere is sufficient evidence to conclude that the population meantest score taking the exam alone is not the same as the populationmean test score taking the exam in a classroom setting.
   • The results are statistically insignificant at αα = 0.01, sothere is insufficient evidence to conclude that the population meantest score taking the exam alone is not the same as the populationmean test score taking the exam in a classroom setting.