Question

Last year, 36% of business owners gave a holiday gift to their employees. This year, a sample of 150 business owners indicated that 45 of them plan to provide a holiday gift to their employees. Using a 0.01 level of significance, would you conclude that the proportion of business owners providing gifts has changed?

Please provide correct answers without using excel formulas.

Answer 1

To Test :-

H0 :- P = 0.36
H1 :- P ≠ 0.36

P = X / n = 45/150 = 0.3

Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.3 - 0.36 ) / ( √(( 0.36 * 0.64) /150))
Z = -1.5309

Test Criteria :-
Reject null hypothesis if Z < -Z(α/2)
Z(α/2) = Z(0.01/2) = 2.576
Z > -Z(α/2) = -1.5309 > -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 the proportion of business owners providing gifts has changed.