Expert: statmaster - 7/28/2009

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.