Question

(EXCEL) DATA 1 :

Participant	Before	After
1	200	180
2	240	165
3	280	215
4	200	220
5	190	145
6	230	250
7	195	175
8	230	185
9	210	140
10	190	172

THE QUESTIONS :

Q1\ The value of the test statisic ?

Q2\ The value of the p value of the test ?

Q3\ What is the H0 rejection region for the testing at the 1% level of significance ? t > ____

Q4/ interpret the result based on your Excel Outputs .

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(EXCEL) DATA 2:

Group 1 Group 2 Group 3 Group 4

44 54 55 44

73 65 78 42

71 79 86 74

60 69 80 42

62 60 50 38

THE QUESTIONS :

Q1\ The value of the test statisic ?

Q2\ The value of the p value of the test ?

Q3\ What is the H0 rejection region for the testing at the 5% level of significance ? F >= ____

Q4/ interpret the result based on your Excel Outputs .

Answer 1

1)

Q1\ The value of the test statisic

Q2\ The value of the p value of the test;

Q3\ What is the H0 rejection region for the testing at the 1% level of significance :

for two tail test.

Q4/ interpret the result based on your Excel Outputs .

Therefore the result is not significant at 1% level of significance.

Therefore we fail to reject the null hypothesis and we do not have sufficient evidence to conclude that the participant has significance difference between before and after the participation.

in order to test whether the participant before after after has any significant change, we define the test hypothesis as:

null hypothesis as:

against the alternative hypothesis as:

( this is two tail test)

the test statistics is define as:

under the null hypothesis t distribution follows degree of freedom.

where and sample standard deviation is

Therefore the test statistics is determined as:

  

Now the t critical value at 1% level of significance at for two tail test is

Therefore the observed t statistics is less than the critical value of the t at 1% level of significance.

and the p value of the test statistics is:

Therefore the result is not significant at 1% level of significance.

Therefore we fail to reject the null hypothesis and we do not have sufficient evidence to conclude that the participant has significance difference between before and after the participation.

Excell output as follows:

2) In oredr to test the null hypothesis that each group has the same mean, we define the test hypothesis as:

against the alternative hypothesis as:

By applying ONE factor ANOVA we get the espected reslt as:

Q1\ The value of the test statisic:

Q2\ The value of the p value of the test:

Q3\ What is the H0 rejection region for the testing at the 5% level of significance:

Q4/ interpret the result based on Excel Outputs .

As

and the p value of the F statistics is

Therefore we reject the null hypothesis and we have sufficient evidence to conclude that the population mean of different groups is differ significantly at 5% level of significance.

t-2.929