The author drilled a hole in a die and filled it with a lead weight, then procee

Question

The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 195 times. Here are the observed frequencies for the outcomes of 12,3,4,5, and 6 respectively: 25, 29, 41, 40, 22, 38. Use a 0.05 significance level to test the claim that the outoomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Does it appear that the loaded die behaves differently than a regular die? O A. Yes, because the test statistic is less than or equal to the critical value. O B. No, because the test statistic is less than or equal to the critical value. C. 0 D. Yes, because the test statistic is greater than the critical value No, because the test statistic is greater than the critical value.

Explanation / Answer

Test statistics, chi-square = 10.3846

p-value = 0.065

critical value of test statistics = 11.07

As test statistics is less than the critical value, we fail to reject the null hypothesis.

Option B is corrrect

Expected frequency Ei Observed Frequency Oi (Oi - Ei)^2/Ei p(1) 32.5 25 1.730769231 P(2) 32.5 29 0.376923077 p(3) 32.5 41 2.223076923 p(4) 32.5 40 1.730769231 p(5) 32.5 22 3.392307692 p(6) 32.5 38 0.930769231 10.38461538

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