QuestionDo 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 \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Alone & 77 & 80 & 78 & 84 & 89 & 86 & 86 & 67 \\ \hline Classroom & 81 & 83 & 90 & 89 & 92 & 89 & 82 & 69 \\ \hline \end{tabular}
Assume a Normal distribution. What can be concluded at the the $\alpha=0.05$ level of significance level of significance?
For this study, we should use Select an answer a. The null and alternative hypotheses would be: $H_{0}$ : Select an answer Select an answer Select an answer
⓪ (please enter a decimal) $H_{1}$ : Select an answer Select an answer Select an answer (t) (Please enter a decimal) b. The test statistic ? $=$ $\square$ (please show your answer to 3 decimal places.) c. The $p$-value $=$ $\square$ (Please show your answer to 4 decimal places.) d. The $p$-value is $\square$ $\alpha$ e. Based on this, we should Select an answer $\square$ $\square$ the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically significant at $\alpha=0.05$, 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 insignificant at $\alpha=0.05$, 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 $\alpha=0.05$, 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 $\alpha=0.05$, 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.