Two Heads Are Better Than One Listed below are brain volumes (cm3 ) of twins.

First Born 1005 1035 1281 1051 1034 1079 1104 1439 1029 1160

Second Born 963 1027 1272 1079 1070 1173 1067 1347 1100 1204

Test the claim at the 5% significance level that the brain volume for the first born is different from the second-born twin.

(a) State the null and alternative hypotheses.

(b) Find the critical value and the test statistic.

(c) Should H0 be rejected at the 5% significance level? Make a conclusion.

(d) Construct a 95% confidence interval for the paired difference of the population means