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 80 American households who have tried to reduce their long-distance bills. Suppose further that of these 80 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:Null Hypothesis : P =0.32 ( Same proportion of American households are trying to reduce long-distance bills by switching companies)

HA: Alternative Hypothesis : P 0.32 ( A significantly different proportion of American households are trying to reduce long-distance bills by switching companies) (Claim)

n = Sample Size = 80

P = Population Proportion = 0.32

Q = 1 - P = 0.68

SE =

= Sample Proportion = 0.22

Test Statistic is given by:
Z = (0.22 - 0.32)/0.2284

= - 0.4379

= 0.01

From Table, critical values of Z = 2.576

Since calculated value of Z = - 0.4379 is greater than criticalvalue of Z = - 2.576, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies.