Question 19

Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 29, 27, 47, 37, 28, 32. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is. (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion. Ho. There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, so the loaded die to behave differently from a fair die. to to be equall WHO . There Insufficient appears appear Do not reject is does not appear do not appear Reject is not Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 ).001 ).004 0.016 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 .103 0.211 4.605 5.991 7.378 9.210 10.597 WN 0.072 0. 115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1.145 1.610 9.236 11.071 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 0.989 1.239 1.690 2. 167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 2. 180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 1.735 2.088 2.700 3.325 4. 168 14.684 16.919 19.023 21.666 23.589 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188