A company produces tires for passenger cars. The quality control manager tells the company president that...

A company produces tires for passenger cars. The quality control manager tells the company president that the proportion of defects is less than 1%. A sample of 36 tires reveals a defect rate of 1.8%. Is there evidence that the quality control manager is lying? Use a .05 level of significance

Solutions

Expert Solution

Given that,
sample size(n)=36
success rate ( p )= x/n = 0.018
success probability,( po )=0.01
failure probability,( qo) = 0.99
null, proportion of defects is less than 1%, Ho:p<0.01
alternate, H1: p>0.01
level of significance, alpha = 0.05
from standard normal table,right tailed z alpha/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.018-0.01/(sqrt(0.0099)/36)
zo =0.4824
| zo | =0.4824
critical value
the value of |z alpha| at los 0.05% is 1.645
we got |zo| =0.482 & | z alpha | =1.645
make decision
hence value of |zo | < | z alpha | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.48242 ) = 0.31475
hence value of p0.05 < 0.31475,here we do not reject Ho
ANSWERS
---------------
null, Ho:p<0.01
alternate, H1: p>0.01
test statistic: 0.4824
critical value: 1.645
decision: do not reject Ho
p-value: 0.31475
we have evidence that proportion of defects is less than 1%

orchestra answered 1 year ago

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