The Organisation for Economic Co-operation and Development (OECD) surveyed 1000 homes at random in each of its member countries in 2014 and found that the number of rooms per person in Canadian homes was 2.5 on average, whereas in the United States it was 2.3. Assume that the standard deviation is 35% of these average values.

Do Canadian homes in general have more rooms per person than homes in the United States? Answer this question:

a) Without pooling the estimates of the standard deviation.

b) With a pooled estimate of the standard deviation.

c) Why is it not possible to use the “paired samples” approach for this question?

d) At which significance level (0.01, 0.05, or 0.1) would your answers to (a) and (b) be different if the OECD had surveyed only 100 homes in each country instead of 1000?