What is the test statistic, critical value, and should you reject Ho? A statisti

Question

What is the test statistic, critical value, and should you reject Ho?

A statistics instructor gave a four-question true-false quiz to his class of 84 students. The results were as follows. The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under this null hypothesis, the number of correct answers has a binomial distribution with 4 trials and success probability 0.5. Perform a chi-square test of this hypothesis. Can you reject H_0 at the alpha = 0.01 level? Use the critical value method with the table. State the null and alternate hypotheses. H_0: The number of correct answers a binomial distribution with 4 trials and success probability 0.5. H_1: The number of correct answers a binomial distribution with 4 trials and success probability 0.5. This hypothesis test is a test.

Explanation / Answer

here test stat =10.9365

critical value at 0.01 level =13.2767

we should not reject HO as test stat is below critical value

observed Expected Chi square Probability O E=total*p =(O-E)^2/E 0 0.063 2.000 5.25 2.01 1 0.250 11.000 21.00 4.76 2 0.375 35.000 31.50 0.39 3 0.250 28.000 21.00 2.33 4 0.063 8.000 5.25 1.44 1 84 84 10.9365

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