Conduct the hypothesis test and provide the test statistic c

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: 26, 28, 43, 38, 29, 36. 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.)

Solution

If the die is fair, then each side is expected to have 200/6 = 33.3333 occurrences.

Thus,

O   E
26   33.33333333
28   33.33333333
43   33.33333333
38   33.33333333
29   33.33333333
36   33.33333333

Using

chi^2 = Sum[(O - E)^2 / E],

chi^2 = 6.7 [ANSWER, ITEM 1]

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The critical value, as df = a - 1 = 6 - 1 = 5, using table/technology,

chi^2(crit) = 12.83250199 [ANSWER, ITEM 2]

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Using technology, the p value as df = 5 is

P = 0.243924643 [ANSWER, ITEM 3]