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 of 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 following table:

Higher scores indicate better performance in creative problem solving. Do the data support the claim that the program of the experimental group promoted creative problem solving? (Use α = 0.01.)
For each hypothesis test, please provide the following information:
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) €“ (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.

Transcribed Image Text:

Twin pair Experimental group 5335 Control group 25 33 47 42 18 21 39 21