Question

For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 55 of the parts from the shipment and finds that 6 parts are defective. If we test to see if the defective proportion is at most 10%, what is the hypothesis?

Answer 1

Let p be the true proportion of defects in the shipment. We test to see if the defective proportion is at most 10%, that is we want to test if p<=0.10.

The following are the hypotheses

The rest of the procedure to test the hypotheses is below

We have the following sample information

n=55 is the sample size which was tested

is the sample proportion of defective parts

is the hypothesized proportion of defective parts

The standard error of proportion is

We can apply the normal approximation as n*p=6 is greater than 5

The test statistics is

This is a right tailed test (The alternative hypothesis has ">"). The p-value of this test is P(Z>0.22) = 0.4129

We will reject the null hypothesis if the p-value is less than the significance level alpha.

Assuming a significance level of 0.05 for this test, we can see that the p-value is greater than the significance level.

Hence we do not reject the null hypothesis.

We can conclude that  the defective proportion is at most 10%.