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):

Category1 2 3 4   Frequency85 58 89 75 

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 4 decimal places and your final answer to 2 decimal places.)

Test statistic

d. What is the conclusion to the hypothesis test? Do not reject H₀ since the value of the test statistic exceeds the critical value.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 does not exceed the critical value.Reject H₀ since the value of the test statistic exceeds the critical value.