Question

A sample of 1300 computer chips revealed that 40% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 37% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.40

H_a : p 0.40

n = 1000

= 0.37

P₀ = 0.40

1 - P₀ = 0.60

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.37 - 0.40 / [(0.40 * 0.60) / 1000]

= -1.94

Test statistic = -1.94

P(z < -1.94) = 0.0261

P-value = 2 * 0.0262 = 0.0524

= 0.02

P-value >

Fail to reject the null hypothesis .