Question

A sample of 16001600 computer chips revealed that 21%21% of the chips fail in the first 10001000 hours of their use. The company's promotional literature states that 23%23% of the chips fail in the first 10001000 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. Is there enough evidence at the 0.020.02 level to support the manager's claim?

signifigant evidence or not enough evidence

Answer 1

n = 1600, = 0.21, p = 0.23, Alpha = 0.02

(a) The Hypothesis:

H0: p = 0.23: The proportion of chips that fail in the first 1000 hours is equal to 0.23.

Ha: p 0.23: The proportion of chips that fail in the first 1000 hours is different from 0.23.

This is a 2 Tailed Test.

The Test Statistic:

The p Value:    The p value (2 Tail) for Z = -1.90 , is; p value = 0.0574

The Critical Value:   The critical value (2 tail) at α = , Zcritical = +2.326 and - 2.326

The Decision Rule:    

The Critical Value Method: If Zobserved is > Zcritical or if Zobserved is < -Zcritical, Then Reject H0.

The p value Method: If the P value is < Alpha, Then Reject H0

The Decision:   

The Critical Value Method: Since Z lies in between +2.326 and -2.326, We Fail To Reject H0

The p value Method: Since P value (0.0574) is > Alpha (0.02), We Fail to Reject H0.

The Conclusion: There is not sufficient evidence at the 98% significance level to conclude that the proportion of chips that fail in the first 1000 hours is different from 0.23.