Three groups of students, 5 in each group, were receiving therapy for severe test anxiety. Group 1 received 5 hours of therapy, group 2 - 10 hours and group 3 - 15 hours. At the end of therapy each subject completed an evaluation of test anxiety (the dependent variable in the study). Did the amount of therapy have an effect on the level of test anxiety? Please develop the appropriate hypothesis test at a .05 level of significance and show and label all steps in your test. The three groups of students received the following scores on the Test Anxiety Index (TAI) at the end of treatment.
TAI Scores for Three Groups of Students
Group 1 - 5 hours Group 2 - 10 hours Group 3 - 15 hours
38 45 41
40 42 42
43 43 40
42 45 43
40 43 40
The solution provides step-by-step method of performing a Analysis of Variance or ANOVA Hypothesis Test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained in details. A separate Excel sheet showing the ANOVA analysis has also been included.
One and Two Tailed Tests: Hypothesis Testing Problem
Ho: u = 50
H1: u not = 50
The sample mean is 49, and the sample size is 36. the population standard deviation is 5. Use the .05 significance level.
a. Is this a one or two tailed test.
b. What is the decision rule?
c. What is the value of the test statistic?
d. What is your decision regarding Ho?
e. What is the p-value? Interpret it.