Question

A sample of 1500 computer chips revealed that 55% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 53% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Answer:

1.28

Step-by-step explanation:

Given that a sample of 1500 computer chips revealed that 55% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 53% of the chips do not fail in the first 1000 hours of their use.

$H_0: p = 0.53\\\\H_a: p \neq 0.53$

(Two tailed test for testing sample proportion with population proportion)

Std error of proportion assuming p = 0.53 is

$\sqrt{0.53*0.47/1000} \\=0.0157$

p difference = 0.02

Z= test statistic = p diff/std error = 1.2775~1.28