A farmequipment manager wanted to compare the average daily

A farm-equipment manager wanted to compare the average daily downtime for 2 sheet metal stamping machines located in 2 different factories. Investigation of company records for 100 randomly selected days on each of the 2 machines gave an average downtime of 12 minutes and a variance of 6 for machine I, while machine II had an average downtime of 9 minutes with a variance of 4.

a) Compute a 90% confidence interval estimate for the true average downtime ?2 - ?1 between machine II and machine I. State any assumptions needed for this interval to be valid.

b) Interpret your confidence interval in terms of the problem. Does the C.I. suggest that one machine has more downtime than the other? How?

Solution

z for 90% CI= 1.64
declare p larger than alpha=0.1 not significant.

mean1 eq: 12 (variance= 36) (se= 0.6)
mean2 eq: 9 (variance= 16) (se= 0.4)

Probability that var1<var2
p=4.0E-5 (left: 1; double: 0)

Difference between means:
M1-M2=12-9=3
sd=9.4706; se=0.7211
90% CI of difference:
1.8139 <3< 4.1861
t-difference: 4.16
df-t: 172; p= 0.99997
(left p: 0; two sided: 0)

As p value is very high we have there is no statistical difference between the two machines.