Question

School Pair	Superintendent School	Matched School
1	63	69
2	63	61
3	61	50
4	76	61
5	66	51
6	79	75
7	45	34
8	79	78
9	51	49

School Pair	Superintendent School	Matched School
10	86	73
11	58	59
12	75	67
13	62	68
14	60	50
15	65	61
16	64	68
17	60	45
18	78	64

Directions: Conduct a T test for Dependent Samples to answer the questions based on the following scenario. (Assume a nondirectional research hypothesis ( two-tailed test) and a level of significance of .05)

To further examine the school performance scores of the district the superintendent identified schools within the district that could be matched to schools from surrounding districts using a series of demographic characteristics such as size, socio-economic status, and percent special education students. The data that were collected are presented above.

1. What are the mean school performance scores for the superintendent's district and matched schools?

2. What are the standard deviations of the school performance scores for the superintendent's district and matched schools?

3. State an appropriate null hypothesis for the analysis.

4. What is the observed or computed value of t?

5. What is the value of degrees of freedom that are reported in the output?

6. What is the reported level of significance from the T Test for Dependent Means?

7. Based on the result of the T Test for Dependent Means, what would you conclude about the difference in scores of schools in the superintendent's district and the matched schools?

8. Present the result as they might appear in an article. This must include a table and narrative statement that reports the results of the T Test for Dependent Means.

Answer 1

1. The mean school performance scores for the superintendent's district and matched schools are 66.167 and 60.167 respectively.

2. The standard deviations of the school performance scores for the superintendent's district and matched schools are 10.65 and 11.63 respectively.

3. The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d ≠ 0

4. The observed or computed value of t is 3.445.

5. The value of degrees of freedom is 17.

6. The reported level of significance from the T-Test for Dependent Means is 0.05.

7. Since the p-value (0.0031) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in scores of schools in the superintendent's district and the matched schools.

8. The calculations are:

School Pair	Superintendent School	Matched School	Difference
1	63	69	-6
2	63	61	2
3	61	50	11
4	76	61	15
5	66	51	15
6	79	75	4
7	45	34	11
8	79	78	1
9	51	49	2
10	86	73	13
11	58	59	-1
12	75	67	8
13	62	68	-6
14	60	50	10
15	65	61	4
16	64	68	-4
17	60	45	15
18	78	64	14
			66.167	mean Superintendent School
			60.167	mean Matched School
			6.000	mean difference (Superintendent School - Matched School)
			7.388	std. dev.
			1.741	std. error
			18	n
			17	df
			3.445	t
			.0031	p-value (two-tailed)