Question

According to a 2015 article, 39% of Americans aged 25 years or older have been arrested. An Orange County police officer feels that this percentage is greater in Orange County. To test this, he randomly selects 150 people living in Orange County who are 25 or older and finds that 65 of them have been arrested. Test the police officer’s claim at the α=0.05 level of significance.

Answer 1

To Test :-

H0 :- P = 0.39
H1 :- P > 0.39

P = X / n = 65/150 = 0.4333

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.433333 - 0.39 ) / √(( 0.39 * 0.61) /150))
Z = 1.0881

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z < Z(α) = 1.0881 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that  percentage is greater in Orange County.