Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Loaded Die?The author 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: 27, 31, 42, 40, 28, 32. Use a 0.05 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?

Solution 11BSC Step 1 By using = 0.05 significance level to test the claim that the outcomes are not equally likely. Expected frequency = 27 + 31 + . .= 33.333 6 The results are listed in the following table. O – observed expected (O – E)² / E E -6.33 27 33.333 1.203 3 -2.33 31 33.333 0.163 3 42 33.333 8.667 2.254 40 33.333 6.667 1.333 -5.33 28 33.333 0.853 3 -1.33 32 33.333 0.053 3 200 199.998 0.002 = 5.860 Expected frequency = 33.333 is same for all categories. The Test Statistic here is (O E )2 2 i i = E i = 5.860 Where O = Observed frequency i Ei Expected frequency