Question

1   26.5
1   28.7
1   25.1
1   29.1
1   27.2
2   31.2
2   28.3
2   30.8
2   27.9
2   29.6
3   27.9
3   25.1
3   28.5
3   24.2
3   26.5
4   30.8
4   29.6
4   32.4
4   31.7
4   32.8

Q1:

• Test for equal variations using the Bartlett test.
Calculating the value of the test statistic
o Finding critical (tabular) values
o Determine the area rejecting the null hypothesis
the decision
Conclusion

Answer 1

Answer:

Bratlett test - using R studio:

Bartlett Test of Homogeneity of Variances

Description
Performs Bartlett's test of the null that the variances in each of the groups (samples) are the same.

## S3 method for class 'formula'
bartlett.test(formula, data, subset, na.action, ...)

######## Excel data ##########

1	26.5
1	28.7
1	25.1
1	29.1
1	27.2
2	31.2
2	28.3
2	30.8
2	27.9
2	29.6
3	27.9
3	25.1
3	28.5
3	24.2
3	26.5
4	30.8
4	29.6
4	32.4
4	31.7
4	32.8

############## Excel data ends ##############

R-codes:

# Read Excel file saved in CSV format
Bdata=read.csv(file.choose(),header = F)

# Conduct Bartlett Test
bartlett.test(V2~V1,Bdata)

#######Test output #######

Bartlett test of homogeneity of variances

data: V2 by V1
Bartlett's K-squared = 0.46564, df = 3, p-value = 0.9264

###########################

Bartlett Test of Homogeneity of Variances

Null hypothesis : Ho : Variance is the same for all 4 groups

Alternative hypothesis : H1 : Variance is the NOT same for all 4 groups

i) Value of statistic : 0.46564

ii) Critical value: Look at below Chi-square table with degrees of freedom=4-1=3, and alpha=0.05

Critical value = 7.815

iii) Area rejecting the null hypothesis is Statistic value > 7.815 ( critical value)

iv) Decision: Since Value of statistic = 0.46564 < Critical value = 7.815 ==> Accept Ho

v) Conclusion: Variance is the same for all 4 groups