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, 26% 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. What is the value of the Test Statistic?

Answer 1

Ho :   p =    0.32                  
H1 :   p ╪   0.32       (Two tail test)          
                          
Level of Significance,   α =    0.01                  
Number of Items of Interest,   x =   20.8                  
Sample Size,   n =    80                  
                          
Sample Proportion ,    p̂ = x/n =    0.2600                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0522                  
Z Test Statistic = ( p̂-p)/SE = (   0.2600   -   0.32   ) /   0.0522   =   -1.150
                             
                          
p-Value   =   0.250 [excel formula =2*NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis       

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