Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. For the context of this problem, μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual.

      Ho:μd=0Ho:μd=0
      Ha:μd≠0Ha:μd≠0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test	post-test
63.4	104.2
65.8	90
18.2	17.8
55.2	54.8
70	34.6
33.1	41.3
24	29.6
49.5	37.4
59.3	96.3
61.5	86.9
54.7	48.5
64.2	34.9
64.9	-7
52.4	71.1
75.8	77.1
54.3	26.1
59.8	118.5
39.7	40.2
59.8	107.7
41.2	8.4

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

Answer 1

x=PreTest

y=post test

μd=PostTest−PreTest

sr.no.	x	y	d=y-x	d- d̅	(d- d̅)2
1	63.4	104.2	40.8	38.22	1460.768
2	65.8	90	24.2	21.62	467.4244
3	18.2	17.8	-0.4	-2.98	8.8804
4	55.2	54.8	-0.4	-2.98	8.8804
5	70	34.6	-35.4	-37.98	1442.48
6	33.1	41.3	8.2	5.62	31.5844
7	24	29.6	5.6	3.02	9.1204
8	49.5	37.4	-12.1	-14.68	215.5024
9	59.3	96.3	37	34.42	1184.736
10	61.5	86.9	25.4	22.82	520.7524
11	54.7	48.5	-6.2	-8.78	77.0884
12	64.2	34.9	-29.3	-31.88	1016.334
13	64.9	-7	-71.9	-74.48	5547.27
14	52.4	71.1	18.7	16.12	259.8544
15	75.8	77.1	1.3	-1.28	1.6384
16	54.3	26.1	-28.2	-30.78	947.4084
17	59.8	118.5	58.7	56.12	3149.454
18	39.7	40.2	0.5	-2.08	4.3264
19	59.8	107.7	47.9	45.32	2053.902
20	41.2	8.4	-32.8	-35.38	1251.744
		Total=	51.6		19659.15
		mean= d̅	Total/20
		d̅=	2.58