Question

A sample of 800 computer chips revealed that 40% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that more than 35% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim? State the null and alternative hypotheses for the above scenario.

Ho:____________________

Ha:____________________

Answer 1

To Test :-

H0 :- P1 = 0.35
H1 :- P1 > 0.35

P0 = 0.35
q0 = 1 - P0 = 0.65
n = 800
P = X / n = 320/800 = 0.4

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.4 - 0.35 ) / √(( 0.35 * 0.65) /800))
Z = 2.965

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.02) = 2.0537
Z > Z(α) = 2.965 > 2.0537, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.965 )
P value = 0.0015
Reject null hypothesis if P value < α = 0.02
Since P value = 0.0015 < 0.02, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the company's claim.