Question

According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 75 American households who have tried to reduce their long-distance bills. Suppose further that of these 75 households, 22% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = .01.

Answer 1

H0: p = 0.32

Ha: p 0.32

Test Statistic :-
Z = ( - p) / ( √( p ( 1 - p) /n)
Z = ( 0.22 - 0.32 ) / ( √(( 0.32 * ( 1 - 0.32) ) /75))
Z = -1.86

Test Criteria :-
Reject null hypothesis if Z < -Z(α/2)
Z(α/2) = Z(0.01/2) = 2.576

Z > -Z(α/2) = -1.8565 > -2.576, we fail to reject the null hypothesis

Conclusion :- We do not have sufficient evidence to support the claim that a significantly different

proportion of American households are trying to reduce long-distance bills by switching companies.