Conduct the hypothesis test and provide the test statistic, critical value and P

Question

Conduct the hypothesis test and provide the test statistic, critical value and P-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: 30, 31, 42, 40, 29, 28. Use a 0.025 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? The test statistic is (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) The P-value is (Round to four decimal places as needed) State the conclusion. H_0. 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.

Explanation / Answer

The statistical software outputf for this problem is:

Chi-Square goodness-of-fit results:
Observed: var13
Expected: All cells in equal proportion

Hence,

Test statistic = 5.5

Critical Value = 12.833

P - Value = 0.3579

Do not reject; is not; appears; does not appear

N DF Chi-Square P-value 200 5 5.5 0.3579

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