Question A company claims that only 1 per cent of its products are faulty. If you took a random sample of 500 products and found that 7 were faulty, would you reject the company's claim? Give reasons for your answer and show any appropriate workings.
The answers should only be derived using any/both the below tools:
1)Z Score
2)Probability
3) t distribution
4) Hypothesis testing
Answer This is an example of one sample testing of hypothesis.
The null hypothesis is Ho:P=0.01 Agianst the alternative H1P≠0.01
where P is proportion of products being faulty.In this case P = 7/500 =0.014 , q=1-p = 0.986
The decision rule to reject HO is if Z>1.96 at 5% level of significance,where
Z = P-P0/sqrt(pq/n)
=(0.014-0.01)/sqrt(0.014*0.986/500)
=0.7612
Since Z<1.96 ,we cant reject Ho.Therfore there is no evidence to reject the company's claim.
