Question

ABC Corporation is considering installing a new assembly procedure. Seven employees of the corporation are randomly selected and the times taken by them to assemble one unit of the product using the existing procedure are recorded. They’re also asked to assemble one unit of the product using the new procedure. The assembly times (in minutes) for these seven selected employees for each procedure are listed in the following table. The production manager of the corporation would like to test whether the new procedure can reduce the mean assembly time when compared with the existing procedure at 2.5% level of significance.

Provide your numerical answers (corrected to 4 decimal places) of the following questions to Moodle.

Employee 1 2 3 4 5 6 7

Existing 64 71 68 66 73 62 70

New 60 66 66 69 63 57 62

a) Sample mean of differences.

b) Test statistic

c) p-value

Answer 1

Sol:

Ho:

Ha:

alpha=0.025

Existing   new   d=new -existing
64   60   -4
71   66   -5
68   66   -2
66   69   3
73   63   -10
62   57   -5
70   62   -8

average   -4.428571429
standard deviation   4.197504928
count   7

a) Sample mean of differences.

= -4.428571429

b) Test statistic

t=Md-0/Sd/sqrt(n)

=( -4.428571429-0)/( 4.197504928/sqrt(7))

t=-2.791396

c) p-value

degrees of freedom=df=n-1=7-1=6

p value in excel for the given test statistic and df

=T.DIST( -2.791396,6,TRUE)

=0.015759719

p=0.0158