Question

Step-by-step explanations are preferred; just the answer doesn't help me learn.

Let’s say we collect data on a sample of 5 people regarding pretest aggression. The aggression measure is on a scale of 1 = low aggression to 10 = high aggression. After initial data collection, we do an intervention aimed at improving self-control and reducing aggression. After the intervention, we measure the same 5 people with the same aggression measure to get a posttest measure of aggression. Here are the (made-up) data…

Subject ID number	Pretest Aggression	Posttest Aggression
1	5	1
2	3	2
3	9	6
4	4	4
5	5	3

We need to determine if pretest aggression significantly differs from posttest aggression and decide to do a dependent-samples t-test. Compute the observed dependent-samples t test value. Report the t test to three decimal places.

Now calculate the degrees of freedom pertaining to the dependent-samples t test.

Our research hypothesis pertaining to the first two questions is that the sample mean of posttest aggression will be lower than the sample mean of pretest aggression. However, we have decided that will be doing a two-tailed test. Our significance level is α = .05. What are the critical t values for the dependent-samples t test in question 5 (specify the sign[s] of the values) and how did you find these critical values?

Based on the answer regarding the observed t value in the first question and the critical t value in the last question, would we reject the null hypothesis or fail to reject the null hypothesis?

Answer 1

Answer Date: 11/02/2019 To test the hypothesis is that pretest aggression significantly differs from posttest aggression at 5% significance level The null and alternative hypothesis is, The t-test statistics is, By using Excel software, find t-test statistics with the help of following steps: 1)Import the data. 2) Select t-test: Paired Two Samples for Means from Data Analysis in Data 3) Select Variable 1 Range and Variable 2 Range. 4) Give Hypothesized Mean Difference. 5) Select Labels and give Alpha. 6) Choose Output Range from Output options 7) Click Ok

t-Test: Paired Two Sample for Means Pretest Aggression Posttest Aggression 5.2 5.2 3.2 3.7 Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 0.729537204 0 4 2.828427125 0.023710328 2.131846782 0.047420656 2.776445105 From the Excel output, the t-test statistics is 2.828 The degree of freedom and the t-critical value for this test is, From the Excel output, the degree of freedom is 4 and the t-critical value for this test is ±2.776

Decision The conclusion region, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that pretest aggression significantly differs from posttest aggression. The result is statistically significant. is that the t value corresponds to sample statistics is fall in the critical