A college professor teaching statistics conducts a study of 17 randomly selected students, comparing the number of homework exercises the students completed and their scores on the final exam, claiming that the more exercises a student completes, the higher their mark will be on the exam. The study yields a sample correlation coefficient of r = 0.496. Test the professor's claim at a 1% significance level.

a.Calculate the test statistic.

t=

Round to three decimal places if necessary

b.Determine the critical value(s) for the hypothesis test.

Round to three decimal places if necessary

c.Conclude whether to reject the null hypothesis or not based on the test statistic.

• Reject
• Fail to Reject

Table 9.3 Student's t-Distribution Table This table is also made available for reference in . . .. the Appendix on page 404. 0 80% confidence 90% confidence 95% confidence 98% confidence 99% confidence dif a= 0.20 a=0.10 a=0.05 a= 0.02 a= 0.01 a/2=0.10 @/2=0.05 @/2=0.025 @/2 =0.01 of2 = 0.005 3.078 6.314 12.706 31.820 63.657 2 1.886 2.920 4.303 6.965 9.925 3 1.638 2.353 3.182 1.541 5.84 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 1.415 1.895 2.365 2.998 3.499 1.39 1.860 2.306 2.897 3.355 g 1.383 1.833 .262 .821 1.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.625 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.584 2.921 17 1.33 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 22 1.321 1.717 .074 2.508 2.819 23 1.319 1.714 2.069 2.500 2.807 24 1.318 1.711 2.064 2.492 1.797 25 1.316 1.708 2.060 2.485 2.787 26 1.315 1.706 2.056 .479 .779 27 1.314 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 .763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 The highlighted value 35 1.306 1.690 2.030 2.438 2.724 shows the critical t-value 40 1.303 1.684 2.021 2.423 2.704 at the 95% confidence level 45 (a/2 =0.025) for a sample 1.301 1.679 2.014 2.412 2.690 with 50 degrees of freedom. 50 1.299 1.676 2.009 2.403 2.678 60 1.296 1.671 2.000 2.390 2.660 70 1.294 1.667 1.994 2.381 2.648 80 1.292 1.664 1.990 2.374 2.639 90 1.291 1.662 1.987 2.369 2.632 100 1.290 1.660 1.984 2.364 2.626 120 1.289 1.658 1.980 2.358 2.617 150 1.287 1.655 1.976 2.351 .609 200 1.286 1.652 1.972 2.345 2.601 100 (2) 1.282 1.645 1.960 2.326 2.576