Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from each pair was part the control group that did not participate in the program to promote creative thinking. At the end of the program, a creative problem-solving test was given, with the results shown in the table below. Twin Pair Experimental group 53 Control Group A B CD E F 35 14 25 33 47 37 Higher scores indicate better performance in creative problem solving. Do the data support the claim that the program of the experimental group did promote creative problem solving? Use a - 0.01. (Let d- experimental - control.) What are we testing in this problem? O single proportion O single mean O difference of means O difference of proportions O paired difference (a) What is the level of significance? State the null and alternate hypotheses. O Ho: Mg- 0; H: Mg0 O Họ: Hg > 0; H: My = 0 O Họ: Mg- 0; H: M <0 O Họ: Mg- 0; H: My > 0 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 < Pvalue < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < P-value < 0.025 O P.value < 0.005