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: 25, 31, 43, 41, 26, 34. Use a 0.10 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.) Enter your answer in the answer box and then click Check Answer parts remaining Clear All Check Answer

Explanation / Answer

applying chi square goodness of fit test:

here test statistic =8.44

critical value =9.236

for above p value =0.1336

as p value is higher then 0.1 level ; failed to reejct null hypothesis

we do not have sufficient evidence to conclude that loaded die behaves differently than a fair die.

observed Expected Chi square Probability O E=total*p =(O-E)^2/E 1 1/6 25.000 33.33 2.08 2 1/6 31.000 33.33 0.16 3 1/6 43.000 33.33 2.80 4 1/6 41.000 33.33 1.76 5 1/6 26.000 33.33 1.61 6 1/6 34.000 33.33 0.01 1 200 200 8.4400

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