In Izmir University of Economics, a statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken in the statistic course. This test was taken by a large group of students in the course, and the average score was 96.9. A random sample of eight students was asked to predict this average score. Their predictions are shown below. Assuming a normal distribution, test the null hypothesis that the population mean prediction would be 96.9. Use a two-sided alternative and a 10% significance level. 74 84 64 63 76 99 85 Upper Critical Values of Student's + Distribution with y Degrees of Freedom Click the icon to view the upper critical values of the Student's t distribution. .X 72 What are the null and alternative hypotheses for this test? O A. Ho u 96.9 H, H = 96,9 0C. H H2 96.9 HH 96.9 For this test at the significance level a with sample mean x, hypothesized mean Ho, sample standard deviation s, and sample size n, what is the form of the decision rule? 156 X-HO X-HO A. Reject H, if s/ Vn n-1a/2 II X-HO OB. Reject H, if >tn - 1,0 s X-Ho O C. Reject Ho if s tra) = wheret, is a Student'st random variable with v degress of freedom. For example, the probability is 10 that a Student's t random variable with 10 degrees of freedom exceeds 1372. PROBABILITY OF EXCEEDING THE CRITICAL VALUE 0.10 0.05 0.025 0.01 0.005 0.001 1 3.078 6.314 12.706 31.821 63.657 318.313 2 1.886 2.920 4.303 6965 9.925 22.327 3 1.638 2.353 3.182 4541 5.841 10.215 4 1.533 2.132 2.776 3.747 4.604 7.173 5 1.476 2.015 2.571 3365 4.032 5.893 6 1.440 1.943 2.447 3.143 3.707 5.208 7 1.415 1.895 2.365 2998 3.499 4.782 8 1.397 1.860 2.306 2.896 3.355 1.490 9 1.383 1.833 2.262 2821 3.250 4.296 10 1.372 1.812 2.228 2.764 3.169 4.143 11 1.363 1.796 2.201 2718 3.106 4.024 12 1.356 1.782 2.179 2.681 3.055 3.929 13 1.350 1.771 2.160 2.650 3.012 3.852 14 1.345 1.761 2.145 2624 2.977 3.787 15 1.341 1.753 2.131 2.602 2.947 3.733 16 1.337 1.746 2.120 2.583 2.921 3.636 17 1.333 1.740 2.110 2.567 2.898 3.646 18 1.330 1.734 2.101 2.552 2.878 3.610 19 1.328 1.729 2.093 2.539 2.861 3.579 20 1.325 1.725 2.086 2.528 2.845 3.552 21 1.323 1.721 2.080 2.518 2.831 3.527 22 1.321 1.717 2.074 2.508 2.819 3.505 23 1.319 1.714 2.069 2.500 2.807 3.485 24 1.318 1.711 2.064 2.492 2.797 3.457 25 1.316 1.708 2.060 2.485 2.787 3.150 26 1.315 1.706 2.056 2.479 2.779 3.435 27 1.314 1.700 2.052 2.473 2.771 3.421 Determine the value(s) for - In-1 tn - 1.a or th- 1,0/2 as appropriate for this test (Round to three decimal places as needed. Use a comma to separate answers as needed.) Calculate the decision statistic X-HO s (Round to three decimal places as needed.) State the conclusion of this test. the null hypothesis. There sufficient evidence that the population mean prediction is not equal to 96.9
