Consider a multinomial experiment with n 272 and k 4. The null hypothesis to be

Question

Consider a multinomial experiment with n 272 and k 4. The null hypothesis to be tested is H : p-p Ps pa 0.25. The observed frequencies resulting from the experiment are (Use Table 3): Category Frequency 77 46 79 70 a. Choose the appropriate alternative hypothesis O All population proportions differ from 0.25 O Not all population proportions are equal to 0.25 b. Calculate the critical value at the 10% significance level (Round your answer to 3 decimal places.) Critical value c. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic d. What is the conclusion to the hypothesis test? O Do not reject H, since the value of the test statistic exceeds the critical value O Reject Ho since the value of the test statistic does not exceed the critical value Do not reject since the value of the test statistic does not exceed the critical value 0 Reject Hu since the value of the test statistic exceeds the critical value.

Explanation / Answer

a) Correct Answer: Option (B)

b) Reject H0: if chisquare value > Critical X^2: 6.251395

Answer : Critical X^2: 6.251395

c) From the given data, we find the expected frequencies and chisquare contribution value as the following table

Answer: Test Statistic, X^2: 10.1471

d) Here Chisquare value > Chisquare critical value, so we reject H0

Answer: Option (D) Reject H0, since the value of the test statistic exceeds the critical value

Observed Expected Freq (Oi) Freq Ei (Oi-Ei)^2 /Ei 77 68 1.191176471 46 68 7.117647059 79 68 1.779411765 70 68 0.058823529 Total: 272 272 10.14705882

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