(Solved): A psychologist has performed the following experiment. For each of 10 sets of identical twins who ...

A psychologist has performed the following experiment. For each of 10 sets of identical twins who were born 30 years ago, he recorded their annual incomes according to which twin was born first. The results (in \( \$ 1,000 \) s) are shown below. Can he infer at \( 5 \% \) significance level that there is a difference in income between the twins? What is the appropriate test to perform? Two-sample test. \( H_{0}: \mu_{1}=\mu_{2} \) versus \( H_{a}: \mu_{1}>\mu_{2} \) Two-sample test. \( \mathrm{H}_{0}: \mu_{1} \neq \mu_{2} \) versus \( \mathrm{H}_{a}: \mu_{1}=\mu_{2} \) Two-sample test. \( \mathrm{H}_{0}: \mu_{1}=\mu_{2} \) versus \( \mathrm{H}_{a}: \mu_{1}<\mu_{2} \) Paired test. \( H_{0}: \mu_{D}=0 \) versus \( H_{a}: \mu_{D} \neq 0 \) Two-sample test. \( H_{0}: \mu_{1}=\mu_{2} \) versus \( H_{a}: \mu_{1} \neq \mu_{2} \) Paired test. \( \mathrm{H}_{0}: \mu_{\mathrm{D}}=0 \) versus \( \mathrm{H}_{\mathrm{a}}: \mu_{\mathrm{D}}>0 \) Paired test. \( H_{0}: \mu_{D} \neq 0 \) versus \( H_{a}: \mu_{D}=0 \) Paired test. \( H_{0}: \mu_{D}=0 \) versus \( H_{a}: \mu_{D}<0 \)