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TestandANOVASunCoast1.docx

Running head: TEST AND ANOVA SUN COAST 1

Test and ANOVA Sun Coast Remediation Data Set

Student’s Name

Instructor’s Name

Course

Date

Data Analysis: Hypothesis Testing

This assignment involves using the Sun Coast Remediation data set to perform statistical tests, in particular, independent samples t test, dependent samples (paired samples) t test as well as ANOVA test. The statistical tables are illustrated.

Independent Samples t Test: Hypothesis Testing

H04: There is no statistically significant difference in variance values for training scores between Group A and Group B.

HA4: There is statistically significant difference in variance values for training scores between Group A and Group B.

Variable 1

Variable 2

Mean

69.79032

84.77419

Variance

122.0045

26.96457

Observations

62

62

Hypothesized Mean Difference

0

df

87

t Stat

-9.66656

P(T<=t) one-tail

9.7E-16

t Critical one-tail

1.662557

P(T<=t) two-tail

1.94E-15

t Critical two-tail

1.987608

The results indicate that the variance values are lower for Group B. The p value is 1.94E-15 < 0.05 (Rumsey, 2011). Therefore, the null hypothesis is rejected and the alternative hypothesis accepted since there is statistically significant difference in variance values between Group A and Group B.

Dependent Samples (Paired Samples) t Test: Hypothesis Testing

H05: There is no statistically significant difference in mean values between pre-exposure and post-exposure.

HA5: There is statistically significant difference in mean values between pre-exposure levels and post-exposure levels.

 

Variable 1

Variable 2

Mean

32.85714

33.28571

Variance

150.4583

155.5

Observations

49

49

Pearson Correlation

0.992236

Hypothesized Mean Difference

0

df

48

t Stat

-1.9298

P(T<=t) one-tail

0.029776

t Critical one-tail

1.677224

P(T<=t) two-tail

0.059553

t Critical two-tail

2.010635

 

The results indicate that the mean values of pre-exposure and post-exposure are almost equal. The results further indicate a p value of 0.06 > 0.05 (Rumsey, 2011). Therefore, the null hypothesis is accepted since there is statistically significant difference in mean values of pre-exposure and post-exposure levels.

ANOVA: Hypothesis Testing

H06: There is no statistically significant difference in yield between means of the variables.

HA6: There is statistically significant difference in yield between means values of the variables.

Anova: Two-Factor Without Replication

SUMMARY

Count

Sum

Average

Variance

Row 1

4

30

7.5

12.33333

Row 2

4

29

7.25

14.25

Row 3

4

29

7.25

14.91667

Row 4

4

31

7.75

5.583333

Row 5

4

25

6.25

4.916667

Row 6

4

32

8

2.666667

Row 7

4

33

8.25

6.916667

Row 8

4

33

8.25

8.916667

Row 9

4

25

6.25

2.25

Row 10

4

31

7.75

3.583333

Row 11

4

32

8

3.333333

Row 12

4

32

8

6

Row 13

4

25

6.25

4.916667

Row 14

4

21

5.25

0.916667

Row 15

4

22

5.5

4.333333

Row 16

4

22

5.5

3

Row 17

4

38

9.5

20.33333

Row 18

4

38

9.5

4.333333

Row 19

4

38

9.5

3.666667

Row 20

4

42

10.5

9

Column 1

20

178

8.9

9.357895

Column 2

20

182

9.1

3.042105

Column 3

20

140

7

6.631579

Column 4

20

108

5.4

1.410526

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Rows

162.7

19

8.563158

2.162605

0.013126

1.771972

Columns

182.8

3

60.93333

15.38857

1.89E-07

2.766438

Error

225.7

57

3.959649

Total

571.2

79

 

 

 

 

Since the p values for rows is 0.01 < 0.05 the null hypothesis is rejected (Rumsey, 2011). Therefore, the alternative hypothesis is accepted.

Reference Rumsey, D. J. (2011). Statistics For Dummies. John Wiley & Sons.