Question

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.

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 ttest value. Report the ttest to three decimal places. HINT: To avoid confusion regarding sign (+/-) of the observed value, subtract the posttest from the pretest to obtain D(pretest-posttest). For full credit, be sure to show all of your work.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d = 0

Alternative hypothesis: u_d ? 0

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = sqrt [ (\sum (d_i - d)² / (n - 1) ]

s = 1.58114

SE = s / sqrt(n)

S.E = 0.70711

DF = n - 1 = 5 -1

D.F = 4

t = [ (x₁ - x₂) - D ] / SE

t = 2.83

where d_i is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 4 degrees of freedom is more extreme than 2.83; that is, less than - 2.83 or greater than 2.83.

Thus, the P-value = 0.047

Interpret results. Since the P-value (0.047) is less than the significance level (0.05), we have to reject the null hypothesis.

Reject H0. The pretest aggression significantly differs from posttest aggression?.