Question

A sample of 1500 computer chips revealed that 71% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 74% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim? State the null and alternative hypotheses for the above scenario.  

Answer 1

Here the claim is that less than 74% chips fail in the first 1000 hours.As the null hypothesis always has an equal sign null and alternate hypothesis are:

Now the test statistic

Degree of freedom =1500-1=1499

P-value for z value(-2.649) and d.f(1499) is 0.004.

As P-value(0.004) is less than alpha(0.05) we reject the null hypothesis

So we have enough evidence to support the claim that under 74% of the chips fail in the first 1000 hours of their use