Question

The data shows process completion times in hours of a manufacturing plant prior to and after a scheduled routine maintenance operation:

A.) Evaluate the assumption of normality of the datasets

B.) State and test the hypothesis of equal variance in the test populations

C.) State and test the hypothesis that the maintenance operation has any effect on the processing time

Before	After
4.17	6.31
5.58	5.12
5.18	5.54
6.11	5.5
4.5	5.37
4.61	5.29
5.17	4.92
4.53	6.15
5.33	5.8
5.14	5.26

Answer 1

A)

Following are the box plots of data:

Box plots are symmetric for both data sets. There is no outliers to any data sets. That is normality can be assumed.

(b)

Following is the output of descritpive statistics:

Descriptive statistics
	Before	After
count	10	10
mean	5.0320	5.5260
sample standard deviation	0.5831	0.4426
sample variance	0.3400	0.1959
minimum	4.17	4.92
maximum	6.11	6.31
range	1.94	1.39

Here we have

Hypotheses are :

Test statistics wil be

Degree of freedom of numerator is df1=n1-1=10-1=9 and degree of freedom of denominator is df2=n2-1=10-1=9.

The p-value is: 0.4239

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. That is we can assume that population variances are equal.

(c)

Here hypotheses are:

Pooled standard deviation is :

and t-statistics will be

Here degree of feedom will be

Test is two tailed so p-value is 0.0469

Since p-value is less than 0.05 so we reject the null hypothesis at 5% level of significance.

The p-value using excel function "=TDIST(2.13,18,2)" is 0.0469.