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: (You may find it useful to reference the appropriate table: chi-square table or F table)

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-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

0.01 p-value < 0.025

p-value 0.10

p-value < 0.01

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.

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.

Reject H0 since the p-value is less than the significance level.

Answer 1

The statistical software output for this problem is :

Not all population proportions are equal to 0.25

Test statistics = 9.446

0.01 p-value < 0.025

Reject H0 since the p-value is less than the significance level.