Consider a multinomial experiment with n = 332 and k = 4. The null hypothesis to

Question

Consider a multinomial experiment with n = 332 and k = 4. The null hypothesis to be tested is H( P3-P4 = 0.25. The observed frequencies resulting from the experiment are (Use Table 3): p-p2- Category Frequency 2 3 4 98 55 88 91 a. Choose the appropriate alternative hypothesis. All population proportions differ from 0.25. 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? Reject Ho since the value of the test statistic exceeds the critical value. Reject Ho since the value of the test statistic does not exceed the critical value Do not reject Ho since the value of the test statistic exceeds the critical value. Do not reject Ho since the value of the test statistic does not exceed the critical value.

Explanation / Answer

The statistical software output for this problem is:

Chi-Square goodness-of-fit results:
Observed: Oi
Expected: All cells in equal proportion

Hence,

a) Alternative Hypothesis: Not all population proportion are equal to 0.25

b) Critical value = 6.251

c) Test statistic = 13.23

d) Conclusion: Option A is correct.

N DF Chi-Square P-value 332 3 13.228916 0.0042

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