Using the following dataset, state the null and alternative hypothesis for two g
ID: 3152304 • Letter: U
Question
Using the following dataset, state the null and alternative hypothesis for two groups, use the independent samples t-test formula to analyze the data, identify the needed critical value to identify the start of the region of rejections (2-tailed test, = .05), make a decision if the null should be rejected or retained. Show all work.
I V=Stress DV=Memory Score (out of 10)
Participants number
Group 1(high stress)
Group 2 (low stress)
1
5
7
2
6
8
3
2
9
4
3
10
5
1
4
Participants number
Group 1(high stress)
Group 2 (low stress)
1
5
7
2
6
8
3
2
9
4
3
10
5
1
4
Explanation / Answer
Given that n1 = 5 n2 = 5
X
(x-X)²
y
(y-Y)²
5
2.56
7
0.64
6
6.76
8
0.04
2
1.96
9
1.44
3
0.16
10
4.84
1
5.76
4
14.44
Total 17
17.2
38
21.4
X = 3.4 Y = 7.6
S2 = 1/n1+n2-2( (x-X)²+ (y-Y)²) =1/8 (17.2 +21.4)=4.8250
The null hypothesis is given by
H0 : µx = µy
Against the alternative hypothesis
H1 : µx µy
The test statistic is given by
t = X - Y/s2/(1/n1)+(1/n2) tn1+n2-2
t = 3.4 – 7.6/(4.8250)/(1/5)+(1/5) t8
t = 4.2 /1.3892
tcal = 3.0232
the tabulated at 0.05 level of significance for two tailed test is 2.31 i.e., ttab = 2.31
here tcal > ttab so we reject the null hypothesis at 0.05 level of significance
X
(x-X)²
y
(y-Y)²
5
2.56
7
0.64
6
6.76
8
0.04
2
1.96
9
1.44
3
0.16
10
4.84
1
5.76
4
14.44
Total 17
17.2
38
21.4
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.