Question

# Consider a multinomial experiment with n = 275 and k = 4. The null hypothesis to...

Consider a multinomial experiment with n = 275 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: (You may find it useful to reference the appropriate table: chi-square table or F table)

Category   1   2   3   4
Frequency   67   55   75   78

a. Choose the appropriate alternative hypothesis.

Not all population proportions are equal to 0.25.
All population proportions differ from 0.25.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

0.025 p-value < 0.05
p-value < 0.01
p-value 0.10
0.01 p-value < 0.025
0.05 p-value < 0.10

c. At the 10% significance level, what is the conclusion to the hypothesis test?

Reject H0 since the p-value is greater than the significance level.
Reject H0 since the p-value is less than the significance level.
Do not reject H0 since the p-value is greater than the significance level.
Do not reject H0 since the p-value is less than the significance level.

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