Problem 3. Cyril Burt (1883 1971), an English educational psychologist who was interested in the possible effect of nurture on nature, studied the intelligence levels of identical twins raised in different conditions. He randomly sampled 27 pairs of identical twins (one raised by birth parents and the other raised in a foster home) and gave them IQ tests. The histograms below show the distributions of IQ scores in the these groups. Some summary statistics, such as sample mean and sample standard devision (SD) are also provided below. Mm Fulcrum 0.3 0.3 02 0.2 5 parents home di'erence mean 0.19 30.1 0.1 SD 7.74 '3 n o n so no 100 120 no no no mo m no lo IO (a) (2 points) Which inference method can be used to test for a difference between the average IQ scores of identical twins raised by birth parents and in a foster home? Write the correct choice and discuss why. (i) Paired t-test (ii) Twosample ttest (iii) Paired Z-test (iv) Two-sample ztest (b) (2 points) Write the apprOpriate hypotheses for this problem. Dene the parameters used. (c) (3 points) What is the rejection region for the test of your choice from part (a) ? (d) (3 points) Compute the pvalue and determine the conclusion of the hypothesis test at 5% signicance level