Question

A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.

Tutoring
Before After
2.4 3.1
2.5 2.8
3.0 3.6
2.9 3.2
2.7 3.5
Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)
t =
Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.)
d =

Answer 1

The test statistic value is, t = -5.245.

The effect size using estimated Cohen's d is 2.35.

Explanation:

A paired t-test would be used to determine whether the remedial tutoring has been effective for the statistics tutor's five students.

The hypothesis can be defined as follows:

H₀: The remedial tutoring has not been effective, i.e. d = 0.

Hₐ: The remedial tutoring has been effective, i.e. d > 0.

Use Excel to perform the Paired t test.

Go to Data → Data Analysis → t-test: Paired Two Sample Means

A dialog box will open.

Select the values of the variables accordingly.

The Excel output is attached below.

The test statistic value is, t = -5.245.

Compute the effect size using estimated Cohen's d as follows:

`\text{Cohen's d}=(Mean_(d))/(SD_(d))`

`=(0.54)/(0.23022)\\\\=2.34558\\\\\approx 2.35`

Thus, the effect size using estimated Cohen's d is 2.35.