Question

A sample of 1600 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that over 31% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim

Answer 1

Answer is given below:

Step-by-step explanation:

given data

sample n = 1600

P = 34 %

p = 31 %

solution

The null and alternative hypothesis are

H0: p = 0.31

Ha: p > 0.31

Test statistics

z = $\hat{p} - p \sqrt{p (1 - p)}{n}$

z = 0.34 - 0.31 $\sqrt{( 0.31 \times 0.69 / 1600)}$

z = 2.59

This is test statistics value.

p-value = P( Z > z)

p-value  = P( Z > 2.59)

p-value = 0.0048

Since p-value < 0.05

level, we have sufficient evidence to reject H03

We conclude at 0.05 level that we have enough evidence t support the claim.