Question

Perform a hypothesis test for the population proportion

A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and that production is not really out of control. At the 0.01 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 3%?

Answer 1

Solution :

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.03

H_a : p > 0.03

= 0.059

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.059 - 0.03/ [(0.03 * 0.97) / 85]

= 1.567

P-value = 0.0585

= 0.01

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that  the percentage of defects exceeds 3% .