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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