A samoie of 16 items provides a sample standard deviation of 9.5. Test the following hypotheses using a: = 0.05. What is your conclusion? Use both the p-value approach and the critical value approach. Hg : 0'3 S 50 Ha : 6'2 > 50 Test statistic = 0 [to 2 decimals) p-value low from table = 6 [to 3 decimals]. Use Table 11.1. pevalue high from table = e (to 3 decimals). Use Table 11.1. x305 = 0 [to 3 decimals] Reject Ho if X3 2 a {to 3 decimals] | Reject the null hypothesis v i M TABLE 11.1 Selected Values from the Chi-Square Distribution Table* Area or probability Xa Degrees Area in Upper Tail of Freedom .99 .975 .95 .90 .10 .05 .025 .01 .000 .001 .004 .016 2.706 3.841 5.024 6.635 .020 .051 .103 .211 4.605 5.991 7.378 9.210 .115 .216 .352 584 6.251 7.815 9.348 11.345 .297 .484 .711 1.064 7.779 9.488 11.143 13.277 DOYOUAWN- .554 .831 1.145 1.610 9.236 11.070 12.832 15.086 .872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 1.647 2.180 2.733 3.490 13.362 15.507 17.535 20.090 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 10 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 11 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 12 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 13 4.107 5.009 5.892 7.041 19.812 22.362 24.736 27.688 14 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 15 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 16 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 17 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 18 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 19 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 20 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 21 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 22 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 23 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 24 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 25 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 26 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 27 12.878 14.573 16.151 18.114 36.741 40.113 43.195 46.963 28 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 29 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 30 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 40 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 60 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 80 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 100 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 "Note: A more extensive table is provided as Table 3 of Appendix B (available online)