A producer is proud of the peaches he grows He claims on ave

A producer is proud of the peaches he grows. He claims, on average, 10% or less in a bushel are defective. You take a sample of 400 and find 50 are defective.

What is the p-value?

If a=.025, will you:

a. fail to reject the null; conclude that the defects are greater than 10%

b. reject the null: conclude that the defects are not greater than 10%

c. Reject the null; conclude defects are greater than 10%

d. fail to reject the null: conclude the defects are not greater than 10%

Solution

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(50/400-0.1)/sqrt(0.1*0.9/400)

=1.67

It is a right-tailed test.

So the p-value= P(Z>1.67) =0.0475 (from standard normal table)

Answer: d. fail to reject the null: conclude the defects are not greater than 10%