The following applies to Questions 1 to 3:

We would like to compare the current unemployment rates in India and Africa. In a random sample of 400 India, 38 of them are found to be unemployed. In a random sample of 300 Africa, 18 are unemployed.

1. What is the margin of error for a 95% confidence interval for the true difference in proportions of India and Africa adults that are unemployed? Keep 6 decimal places in intermediate calculations and report your final answer rounded to 3 decimal places.

2. We conduct a hypothesis test of Ho: Pc = Pu Vs. Ha: Pc Pu to compare the unemployment rates in the two countries . The value of the z test statistic is: Keep 6 decimal places in intermediate calculations and report your final answer rounded to 2 decimal places.

3. The two proportion z test in the previous question can also be conducted as a chi square test of homogeneity. At the 5% level of significance, what can we conclude about homogeneity of the population proportions of Canadians and Americans who are unemployed?

a. There is insufficient evidence they are homogeneous

b. There is sufficient evidence that they are homogeneous.

c. There is sufficient evidence that they are not homogeneous.

d. There is insufficient evidence that they are not homogeneous.

4. The table below shows the proportion of votes received by the various political parties in the 2019 Manitoba provincial election:

Party CG CPP BJP Other

Proportion of Votes 0.47 0.31 0.14 0.08

We would like to conduct a chi-square goodness of fit test to determine whether party support has changed since the last election.

In a random sample of 500 voters, 200 say they now support the CG, 210 support the CPP, 60 support the BJP, and 30 support other parties. What is the value of the test statistic for the appropriate test of significance?