Question

6. A manufacturer claims that a customer will nd no more than 8% defective knee braces in a large shipment. A customer decides to test this claim after reading an article in the American Journal of Sports Medicine, which discusses the force exerted on a knee brace used for injured athletes and convinces the customer that high quality is essential. A random sample of 200 braces is selected from the shipment, and 28 defectives are found. Test the manufacturer's claim at a .01 level of significance. What are the null hypothesis and Decision rule?

Answer 1

Solution:

For the given scenario, the null and alternative hypotheses are given as below:

Null hypothesis: H0: There are no more than 8% defective knee braces in a large shipment.

Alternative hypothesis: Ha: there are more than 8% defective knee braces in a large shipment.

H0: p ≤ 0.08 versus Ha: p > 0.08

This is an upper tailed test.

We are given

α = 0.01

So, critical Z value = 2.3263

(by using z-table)

Decision rule: Reject the null hypothesis when test statistic Z > 2.3263