Question

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.

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 the αα = 0.01 level of significance level of significance?

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

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

H0:H0:  Select an answerμdμ1p1 ?=<>≠ Select an answer0μ2p2 (please enter a decimal)   

H1:H1:  Select an answerp1μdμ1 ?=><≠ Select an answer0μ2p2 (Please enter a decimal)

2. The test statistic ?tz = (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 ?≤> αα
5. Based on this, we should Select an answeracceptrejectfail to reject the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 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 significant at αα = 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.
   • The results are statistically significant at αα = 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 insignificant at αα = 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.

Answer 1