#14- need help show full work psych stats ### Problem 14: Statistical Hypothesis Testing**a. Repeated-Measures Study Analysis**- A study conducted with 8 participants results in a mean difference (\(M_D\)) of 3, with a variance (\(s^2\)) of 72.- Perform a two-tailed hypothesis test using an alpha level (\(\alpha\)) of 0.05.- Goal: Determine the likelihood of this sample originating from a population where the mean difference (\(\mu_D\)) is zero.**b. Hypothesis Testing with Increased Mean Difference**- Assume the mean difference (\(M_D\)) is now 9.- Again, conduct a two-tailed hypothesis test with \(\alpha = 0.05\).- Determine if it is likely this sample is from a population with \(\mu_D = 0\).**c. Influence of Sample Size**- Discuss how sample size affects the detection of a significant mean difference. Consider the impact on statistical power and the ability to find significant results.

Given sample size n=8Mean difference Md=3variance s2=72level of significance Given data is taken from repeated measures of study.So perform a paired t-test for the given problem.Null hypothesis H0:The sample is coming from the population.Alternative hypothesis H1: The sample is not coming from the population.test statistic:Critical value of t taken from Excel using the function "=T.DIST.INV.2T("For the given problem Excel function is "=T.DIST.INV.2T("=2.3646t calculated =1t critical value =2.3646tcal<tcriSo null hypothesis is accepted.The sample is coming from the population.Given data is taken from repeated measures of study.So perform a paired t-test for the given problem.Null hypothesis H0:The sample is coming from the population.Alternative hypothesis H1: The sample is not coming from the population.test statistic:Critical value of t taken from Excel using the function "=T.DIST.INV.2T("For the given problem Excel function is "=T.DIST.INV.2T("=2.3646t calculated =3t critical value =2.3646tcal>tcriSo null hypothesis is rejected.The sample is not coming from the population.c) From part(a),and part (b), it is clear that as the sample mean difference increase there is a chance to reject the null hypothesis.Therefore increased sample mean difference will influence the likelihood of finding a significant mean difference.a) The sample came from the population with b)The sample did not come from the population with c) From part(a), and part (b), it is clear that as the sample mean difference increase there is a chance to reject the null hypothesis.Therefore increased sample mean difference will influence the likelihood of finding a significant mean difference.