Question

Suppose there is a random sample of 400 observations, divided into four groups. The table below summarizes the count of observations that were seen in each group. Group 1 160 Group 2 120 Group 3 40 Group 4 80 = P2 = pz = PA = 0.25, against the alternative hypothesis We are interested in testing the null hypothesis Ho: P HA: At least one proportion is incorrect a) What is the expected count for each of the groups? Expected: Number b) What is the value of the test statistic? Round your response to at least 2 decimal places. Number c) What are the appropriate degrees of freedom? Number d) What conclusion can be made at the 5% level of significance? There is very strong evidence against the null hypothesis, and therefore it is rejected in favour of the alternative hypothesis that at least one proportion is not equal to 0.25. There is no significant evidence against the null hypothesis, and therefore there is no significant evidence that any of the proportions is not equal to 0 0.25

Answer 1

The statistical software output for this problem is:

Hence,

a) Expected = 100

b) Test statistic = 80

c) Degrees of freedom = 3

d) Option A is correct.