[50points] At Suntronic, you are responsible for selecting the manufacturing pro

Question

[50points] At Suntronic, you are responsible for selecting the manufacturing process that yields intraocular lens with the least variability/variance in terms of optical power (diopters). At this point, you don't know which (if either) process yields samples with a higher variance (hint: pick correct alternate hypothesis). Are you able to select the process with the least variance with 98% confidence? write both the null and alternate hypotheses. The descriptive statistics are as follows: 1. Fabrication Process 1:S,-0.23 diopters, ni = 31 b. Fabrication Process 2: S2 0.30 diopters, n2 25 a.

Explanation / Answer

Given that,
sample 1
s1^2=0.0529, n1 =31
sample 2
s2^2 =0.09, n2 =25
null, Ho: ^2 > ^2
alternate,the manfacturing process that
yields intraocular lens with the least variability/variance H1: ^2 < ^2
level of significance, = 0.02
from standard normal table,left tailed f /2 =2.297
since our test is left-tailed
reject Ho, if F o < -2.297
we use test statistic fo = s1^1/ s2^2 =0.0529/0.09 = 0.59
| fo | =0.59
critical value
the value of |f | at los 0.02 with d.f f(n1-1,n2-1)=f(30,24) is 2.297
we got |fo| =0.588 & | f | =2.297
make decision
hence value of |fo | < | f | and here we do not reject Ho
ANSWERS
---------------
null,the manfacturing process that
yields intraocular lens with the strong variability/variance Ho: ^2 > ^2
alternate,the manfacturing process that
yields intraocular lens with the least variability/variance H1: ^2 < ^2
test statistic: 0.59
critical value: -2.297
decision: do not reject Ho

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