Consider a multinomial experiment with n = 260 and k = 4. The null hypothesis to

Question

Consider a multinomial experiment with n = 260 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are (Use Table 3): Category 1 2 3 4 Frequency 73 44 75 68 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 9.26 d. What is the conclusion to the hypothesis test? Reject H0 since the value of the test statistic does not exceed the critical value. Do not reject H0 since the value of the test statistic exceeds the critical value. Do not reject H0 since the value of the test statistic does not exceed the critical value. Reject H0 since the value of the test statistic exceeds the critical value.

Explanation / Answer

a) Alternative hypothesis:

Not all population proportions are equal to 0.25.

b) Degrees of freedom = n - 1 = 4 - 1 = 3

So,

Critical value at 10% significance level = 6.251

c) The statistical software output for this problem is:

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

Hence,

Test statistic = 9.45

d) Reject H0 since the value of the test statistic exceeds the critical value. Option D is correct.

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