Researchers are interested to see if there is a difference in average retirement age between India and France.

(a) In a random sample of 30 retired French workers, the average age of retirement was 64 years, with standard deviation 10 years. In a separate sample of 100 retired Indian workers, the average age of retirement was 61 years, with standard deviation 5 years. perform a hypothesis test of the researcher's hypothesis using a significance level of 0.05.

(b) Repeat the hypothesis test from (a), but now suppose that researchers sampled 1000 retired Indian workers instead (assume the mean and standard deviation don't change). Comment on anything interesting you notice.