Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study by Tramo, Loftus, Stukel, Weaver, and Gazzaniga were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.

1. Let $\displaystyle \mu_{{1}}$ and $\displaystyle \mu_{{2}}$ represent the mean Full Scale IQ score for all first-born identical twins and second-born identical twins, respectively, and let $\displaystyle \mu_{{d}}$ be the mean of the differences in IQ score of all identical twins (IQ score of first-born twin - IQ score of second-born twin).
   
   Which are the appropriate null and alternative hypotheses?
   
   
   • (A)

     H₀: μ_d = 0

     H_a: μ_d > 0

   • (B)

     H₀: μ_d = 0

     H_a: μ_d < 0

   • (C)

     H₀: μ_d > 0

     H_a: μ_d = 0

   • (D)

     H₀: μ₁= μ₂

     H_a: μ₁ > μ₂

   • Both (A) and (D) are correct.
   
   
   

2. The following is the (edited) output for the test:
   
   

   From the output we learn that:
   
   

   • The data provide sufficient evidence to reject H₀ and, thus, conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.
   • The data provide sufficient evidence to reject H₀. We therefore conclude the data do not provide evidence to conclude that the mean Full Scale IQ scores for first-born identical twins is higher than that of second-born identical twins.
   • The data do not provide sufficient evidence to reject H₀. We therefore conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.
   • The data do not provide sufficient evidence to reject H₀. In other words, based on the data we cannot conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.