Question

A hospital director believes that more than 29% of the lab reports contain errors and feels an audit is required. A sample of 300 reports found 99 errors. Is there sufficient evidence at the 0.02 level to substantiate the hospital director's claim? State the null and alternative hypotheses for the above scenario.

Answer 1

To Test :-

H0 :- P = 0.29
H1 :- P > 0.29

P = X / n = 99/300 = 0.33

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.33 - 0.29 ) / √(( 0.29 * 0.71) /300))
Z = 1.5268

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.02) = 2.054
Z < Z(α) = 1.5268 < 2.054, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.5268 )
P value = 0.0634
Reject null hypothesis if P value < α = 0.02
Since P value = 0.0634 > 0.02, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evience to support the hospital director's claim.