a. Let µi and µ2 represent the mean Full Scale IQ score for all first-born identical twins and second- born identical twins, respectively, and let µa 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? O (A) Họ: Ha = 0 Hg: Hg > 0 O (B) Họ: Hg = 0 Hg: Ho < 0 O (C) Họ: Hg > 0 Hạ: Ha = 0 O (D) Ho: H1= P2 H3: H1 > Hz O Both (A) and (D) are correct. b. The following is the (edited) output for the test: Paired T-Test and CI Sample First-born Mean StDev SE Mean 10 10 10 70.6 78.0 -0.43 23.4 17.4 11.83 7.4 5.5 3.74 Second-born Difference 95% lower bound for mean difference: -7.29 T-Test of mean difference = 0 (vs > 0): T-Value - -0.11 P-Value - 0.544 From the output we learn that: O The data provide sufficient evidence to reject H, 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. O The data provide sufficient evidence to reject Ho- 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. O The data do not provide sufficient evidence to reject Ho. 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. O The data do not provide sufficient evidence to reject Ho. 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.

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A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.