Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 39 orders that were not accurate among 330 orders observed. Use a 0.10 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable?

Answer 1

H0: p = 0.10

Ha: p 0.10

Sample proportion = X / n = 39/330 = 0.1182

Test Statistic :-
Z = ( - p) / ( √((p ( 1 - p))/n)
Z = ( 0.1182 - 0.1 ) / ( √(( 0.1 * 0.9) /330))
Z = 1.10

Test Criteria :-

Reject null hypothesis if Z > Z(α/2)
Z(α/2) = Z(0.1/2) = 1.645

Z < Z(α/2) = 1.101 < 1.645,

fail to reject the null hypothesis

Conclusion :- We have sufficient evidence to say that the accuracy rate appear to be​ acceptable