Question

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 146. What is the probability that the sample proportion will be within 9 percentage points of the population proportion?

(Tip: If you compute the standard error [i.e. the standard deviation of the sampling distribution], round it to 4 digits if you have to use it in later computations.)

Answer =  (Enter your answer as a number accurate to 4 decimal places.)

Answer 1

population proportion ,p=   0.75                                  
n=   146                                  
                                      
std error , SE = √( p(1-p)/n ) =    0.0358                                  
                                      
we need to compute probability for                                       
0.66   < p̂ <   0.84                              
                                      
Z1 =( p̂1 - p )/SE= (   (0.66-0.75)/0.0358)=       -2.514                          
Z2 =( p̂2 - p )/SE= (   (0.84-0.75)/0.0358)=       2.514                          
P(   0.66   < p̂ <   0.84   ) = P(   -2.514   < Z <   2.514   )      
= P ( Z <   2.514   ) - P (    -2.514   ) =    0.9940   -   0.0060 =   0.9881   (answer)

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