Question

According to the U.S. Census Bureau, 7.1% of Americans living in 2004 were between the ages of 20 and 24. Suppose that a random sample of 400 Americans taken this year yields 35 between the ages of 20 and 24. Test whether the population proportion of Americans aged 20 –24 is different than the 2004 proportion, using significance level ?=0.01

Answer 1

To Test :-

H0 :- P = 0.071
H1 :- P ≠ 0.071

P = X / n = 35/400 = 0.0875

Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.0875 - 0.071 ) / ( √(( 0.071 * 0.929) /400))
Z = 1.2849

Test Criteria :-
Reject null hypothesis if Z > Z(α/2)
Z(α/2) = Z(0.01/2) = 2.576
Z < Z(α/2) = 1.2849 < 2.576, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that population proportion of Americans aged 20 –24 is different than the 2004 proportion.