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. Aperson 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, 46, 40, 27, 31. Use a 0.01 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.)

Explanation / Answer

H0: The outcome are equally likely

H0: The outcome are not equally likely

Let the los be alpha = 0.01

The expected frequencies are calcualted as 200/6 = 33.333 for all.

The chisquare contribution values are

From the given data

Test Statistic, X^2: 9.2800
Critical X^2: 15.08626
P-Value: 0.0984

Here P-value > alpha 0.01, so we accept H0

There is not sufficient evidence to support the claim that the outcome are not equally likely. The outocmes are equally likely, so that loaded dies not differ from a fair die

Observed Expected Outcomes freq (Oi) freq (Ei) (Oi-Ei)^2/Ei 1 29 33.33333 0.563333333 2 27 33.33333 1.203333333 3 46 33.33333 4.813333333 4 40 33.33333 1.333333333 5 27 33.33333 1.203333333 6 31 33.33333 0.163333333 Total = 200 200 9.28

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