Question

A sample of 14001400 computer chips revealed that 311% of the chips do not fail in the first 10001000 hours of their use. The company's promotional literature claimed that more than 28(% do not fail in the first 10001000 hours of their use. Is there sufficient evidence at the 0.050.05 level to support the company's claim

Answer 1

There is sufficient evidence at 0.05 significant level to support company's claim.

Explanation:

We have these informations from the question

n = 1400

P^ = 31% = 0.31

Alpha level = 5% = 0.05

Then we come up with the hypothesis

H0: P = 0.28

H1: P>0.28

From here we calculate the test statistic

z = p^ - p/√pq/n

P = 0.28

q = 1-0.28

= 0.72

z = 0.31-0.28/√(0.31*0.72)/1400

= 0.03/√0.0001594

= 0.03/0.012

= 2.5

Then we have a p value = 0.00621

The p value is less than significance level

0.00621<0.05

So the null hypothesis is rejected.

We conclude that There is sufficient evidence at 0.05 significant level to support company's claim.