The variance in a production process is an important measure of the quality of t
ID: 3208333 • Letter: T
Question
The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance.
Machine 1 Machine 2 2.95 3.22 3.45 3.30 3.50 3.34 3.75 3.28 3.48 3.29 3.26 3.25 3.33 3.30 3.20 3.27 3.16 3.38 3.20 3.34 3.22 3.35 3.38 3.19 3.90 3.35 3.36 3.05 3.25 3.36 3.28 3.28 3.20 3.30 3.22 3.28 2.98 3.30 3.45 3.20 3.70 3.16 3.34 3.33 3.18 3.35 3.12Explanation / Answer
Given that,
sample 1
s1^2=0.048889, n1 =25
sample 2
s2^2 =0.005901, n2 =22
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.05
from standard normal table, two tailed f /2 =2.368
since our test is two-tailed
reject Ho, if F o < -22 OR if F o > 2.368
we use test statistic fo = s1^1/ s2^2 =0.048889/0.005901 = 8.28
| fo | =8.28
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(24,21) is 2.368
we got |fo| =8.285 & | f | =2.368
make decision
hence value of | fo | > | f | and here we reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 8.28
critical value: -2.368 , 2.368
decision: reject Ho
we have evidence to support there is a significant difference between the variances in the bag weights for the two machines
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