PLEASE EXPLAIN STEPS this is my third time posting this ques

PLEASE EXPLAIN STEPS, this is my third time posting this question because the previous answers dont make sense.

Researchers are interested in testing whether cognitive behavioral therapy (CBT) can reduce the social anxiety of highly anxious people. They recruited 18 sets of identical twins, both of whom suffered from similar levels of social anxiety prior to the study and neither of whom had ever underwent any kind of therapy. For each set of twins, the researchers randomly assigned one twin to receive CBT and the other twin continued to receive no therapy. After two months have passed, the researchers measured the twins\' self-reported social anxiety. The social anxiety scores are shown to the right. Assume that the social anxiety scores are normally distributed and that lower scores denote lower levels of social anxiety. At the = 0.05 level of significance, is there evidence to suggest that CBT is effective at reducing social anxiety?

Suppose this same design were to be repeated, but instead of 18 sets of identical twins, the researchers were able to recruit 4,000 sets of identical twins. Suppose further that under this new study, the researchers found that twins who had undergone CBT had significantly lower social anxiety scores than twins who had received no therapy at the = 0.01 level of significance. The researchers contend that their study provides causal evidence that CBT is effective at lowering social anxiety for the participants in their study. Given the design of the study, do you agree with their conclusion? Why or why not?

Solution

H0: mu1 = mu2

Ha: mu1 >mu2

Right tailed test for a paired test

The T-value is 0.797599.

The P-Value is 0.430639.

The result is not significant at p < 0.05.

Hence accept null hypothesis that the two means are equal.

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When sample size increases Std error decreases hence margin of error also decreases.

For alpha = 0.01, p value is less than 0.01

As large sample size gives more accurate results, repeat two more times the same test with large sample size and conclude.