Question

As a manufacturing engineer you have installed a new process. This process you feel improved the assembly time of the device.

You have gathered the following "old process" time and "new process" time. All times are in minutes. Assume the population of paired differences is approximately normally distributed.

The findings are in the following table.

OLD	NEW
73	60
69	66
72	66
66	69
73	63
68	57
70	62

Use the 95% confidence interval for mu differences

1. What is the sum of the differences?

2.  What is the average d-bar of the differences? (three decimals)

3.  What area is in each tail?

4.  What is the standard deviation of the differences?

5.  What is the degrees of freedom ?  

6.  What is the t-value? (three decimals)

7.  What is the t-value times Sd / sqrt (n)?   (three decimals)

8.  What is the low estimate of improvement? (three decimals)

9.  What is the high estimate of improvement?   (three decimals)

Answer 1

Old(x1)	New(x2)
73	60	13	37.735
69	66	3	14.877
72	66	6	0.735
66	69	-3	97.162
73	63	10	9.878
68	57	11	17.164
70	62	8	1.306

1) Sum of differences =

2) Average of differences

             (Round to 3 decimal)

3) Area in each tail:

Confidence level = c = 0.95

alpha = 1 - c = 1 - 0.95 = 0.05

left tail area = 0.05/2 = 0.025

right tail area = 0.05/2 = 0.025

4) Standard deviation of differences:

                               (Round to 4 decimal)

5) Degrees of freedom = n -1 = 7 - 1 = 6

6) t value for c = 0.95 and degrees of freedom = 6 is

tc = 2.447                      (From statistical table of t values)

7)

          (Round to 3 decimal)

8) Lower estimate

= 1.807

Lower estimate = 1.807

9)

Upper estimate

= 11.907

Upper estimate = 11.907