Question

A sample of 1100 computer chips revealed that 70% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 73% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Is there enough evidence at the 0.05 level to support the manager's claim?

Answer 1

Let X be the event that chips do fail in the first 1000 hours of use. From the sample information we know that

We have to test the claim whether the actual percentage of failing is equal to 73% or not

This is a binomial proportion hypothesis testing

Where p is the population proportion and = 73%

This is 2 tailed hypothesis testing.

Test Statistic =

Substituting the values

= 2.1712

Critical value at

Decision Criteria : If Test Stat > Critical V, we reject the null hypothesis.

2.1712 > 1.96

Decision: Since T.S > C.V., we do have sufficient evidence to reject the null hypothesis (manager's claim) at 5% level of significance.

Conclusion: We are 95% confident that the actual percent of chips failing after use of 1000 hours is not 73%.