Additional problem using the independent t-test

Let's do an additional problem involving the independent t test, to make certain that we know how to do it. For this problem lets use one from the textbook and see if we get the same answer as the text did. The problem is on pages 179-184 of the text.

Research Problem: A new test preparation company, called Bright Future (BF), wants to convince high school students studying for the American College Testing (ACT) assessment test that enrolling in their test preparation course would significantly improve the students' ACT scores. BF selects 10 students at random and assigns five to the experimental group and five to the control group. The experimental group students participate in the test preparation course conducted by BF. At the conclusion of the course, both groups of students take the ACT test form which was given to high school students the previous year. BF conducts a t-test for independent samples to compare the scores of Group 1 (Experimental, E) to those of Group 2 (Control, C).

Let's put this data into an Excel Worksheet and then calculate the value of the independent t:

Looking at the data we calculated we can see the the means for the two groups (24 and 18) are the same as those reported in the text. The value of t Stat is 2.25175988 which we can round off to 2.252, which is similar to the value reported in the text as 2.26. Since this problem is concerned only with the Experimental Group having a higher mean than the Control Group, it would be a one-tailed test and we can read the critical value of t in the t Critical one-tail row as 1.85954832 which rounds off to 1.860, which is the same value reported in the text.

We have all the information we need to complete the six step statistical inference process:

1. State the null hypothesis and the alternative hypothesis based on your research question.
   
   
2. Set the alpha level.
   
3. Calculate the value of the appropriate statistic. Also indicate the degrees of freedom for the statistical test if necessary.
   t = 2.252
   df = n₁ + n₂ - 2 = 5 + 5 - 2 = 8
4. Write the decision rule for rejecting the null hypothesis.
   Reject H₀ if t is >= 1.860
5. Write a summary statement based on the decision.
   Reject H₀, p < .05, one-tailed
6. Write a statement of results in standard English.
   Students who participated in the test-taking course, scored significantly higher on the practice form of the ACT, than did the control group of students.