Question

A statistics teacher 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 3.0 2.5 2.9 3.0 3.6 2.9 3.1 2.7 3.5 (a) 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 = Incorrect: Your answer is incorrect. State the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. Correct: Your answer is correct. (b) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.) d =

Answer 1

The tutoring is effective if the average grades after tutoring is greater than before tutoring

Average of (Grades after tutoring - Graders before tutoring ) > 0

Population Average difference in grades (After - Before)

Null hypothesis :

Alternate Hypothesis : : Right taile test

di : Grades after - Grades after

n : sample size =5

Before	After	d: (After - Before)	d-d	(d-d)2
2.4	3	0.6	0.08	0.0064
2.5	2.9	0.4	-0.12	0.0144
3	3.6	0.6	0.08	0.0064
2.9	3.1	0.2	-0.32	0.1024
2.7	3.5	0.8	0.28	0.0784
	Total	2.6		0.208
	Mean	=2.6/5 =0.52

Sample Mean of the differences :	0.52
Sample Standard Deviation of the differences : sd	0.228
Sample Size : n	5
Level of significance :	0.05
Degrees of Freedom : n-1	4

Right Tailed Test: p-value

As P-Value i.e. is less than Level of significance i.e (P-value:0.0035 < 0.05:Level of significance); Reject Null Hypothesis

reject the null hypothesis

(b) effect size using estimated Cohen's d

X₁ : Sample grades After turoting

X₂ : Sample grades before tutoring

n =5 : sample size

n1: Sample size of after =5

n2 : sample size of before = 5

M_after : Mean of the grades after tutoring =

M_before : Mean of the Grades before tuoring:

	Before:X1	After:X1	X1-	(X2-	X1-	(X1-
	2.4	3	-0.3	0.09	-0.22	0.0484
	2.5	2.9	-0.2	0.04	-0.32	0.1024
	3	3.6	0.3	0.09	0.38	0.1444
	2.9	3.1	0.2	0.04	-0.12	0.0144
	2.7	3.5	0	0	0.28	0.0784
Total	13.5	16.1		0.26		0.388
Mean	2.7(M2)	3.22(M1)

d = 1.8271