Question

Consider a multinomial experiment with n = 300 and k = 4. If we want to test whether some population proportions differ, then the null hypothesis is specified as H0

a. p1=p2=p3=p4=0.20
b. μ1=μ2=μ3=μ4=0.25
c. μ1=μ2=μ3=μ4=0.20
d. p1=p2=p3=p4=0.25

Answer 1

Explanation:

The correct answer is d. p1=p2=p3=p4=0.25.

In a multinomial experiment, the null hypothesis specifies the values of the population proportions for each category. Therefore, options (a), (b), and (c) cannot be the null hypothesis since they specify values for the population means, not the population proportions.

Option (d) specifies that all population proportions are equal to 0.25, which is a valid null hypothesis for a multinomial experiment with four categories.