Ex: The quality control manager at a bottling plant is concerned about the varia

Question

Ex: The quality control manager at a bottling plant is concerned about the variability of filledbottles. Regulations specify that the standard deviation of the amount of fill cannot exceed 0.1ounce. To determine whether the process is meeting this specification, ten bottles arerandomly selected and their contents are weighed. If the specification is not met, the bottlingprocess must be shut down.

11.59    11.97    12    12.03    12.02    12.1    11.97    11.97    12.02    12

A. Should the manager shut down the bottling process? Use a 5% significance level.

Explanation / Answer

Given that,
population standard deviation ()=0.1
sample standard deviation (s) =0.1381
sample size (n) = 10
we calculate,
population variance (^2) =0.01
sample variance (s^2)=0.01907161
null, Ho: =0.01
alternate, H1 : <0.01
level of significance, = 0.05
from standard normal table,left tailed ^2 /2 =16.919
since our test is left-tailed
reject Ho, if ^2 o < -16.919
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(10 - 1 ) * 0.01907161 / 0.01 = 9*0.01907161/0.01 = 17.16
| ^2 cal | =17.16
critical value
the value of |^2 | at los 0.05 with d.f (n-1)=9 is 16.919
we got | ^2| =17.16 & | ^2 | =16.919
make decision
hence value of | ^2 cal | > | ^2 | and here we reject Ho
^2 p_value =0.0463

ANSWERS
---------------
null, Ho: =0.01
alternate, H1 : <0.01
test statistic: 17.16
critical value: -16.919
p-value:0.0463
decision: reject Ho

standard deviation of the amount of fill cannot exceed 0.1ounce

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