November 15, 2017 Confidence Interval and Hypothesis Test on the Proportion comp
ID: 3364863 • Letter: N
Question
November 15, 2017 Confidence Interval and Hypothesis Test on the Proportion composites manufacturer is having serious problems with porosity in their parts. A Quality Engineer 1. A samples 300 parts and finds 58 defective. (a) Test the hypothesis that defective rate (proportion defective) exceeds IS%. Test at a-0.05 What assumptions are made? Show mathematical evidence to support What is the parameter of interest? assumption. Write the null and alternative hypotheses. Calculate the test statistic Determine the reject region. Find the p-value. Show normal graph including reject region and test statistic Make a decision and write a thorough interpretation in context of the problem. If in reality the true proportion defective is 12%, what type of error, if any, occurred?Explanation / Answer
Given that,
possibile chances (x)=58
sample size(n)=300
success rate ( p )= x/n = 0.1933
success probability,( po )=0.15
failure probability,( qo) = 0.85
null, Ho:p=0.15
alternate, H1: p>0.15
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.19333-0.15/(sqrt(0.1275)/300)
zo =2.102
| zo | =2.102
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.102 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.10198 ) = 0.01778
hence value of p0.05 > 0.01778,here we reject Ho
ANSWERS
---------------
a.
testing the defective rate in the provided sample
null, Ho:p=0.15
alternate, H1: p>0.15
test statistic: 2.102
reject Ho, if zo > 1.64
critical value: 1.64
decision: reject Ho
p-value: 0.01778
we have evidence that defective is above 15%
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