Question

B. The proportion of customers who are completely satisfied in a recent satisfaction survey of 300 customers at XYC Inc. is found to be 0.26. Test the hypothesis that the population proportion of customers who are completely satisfied is greater than 0.22 using the critical value approach and a 0.05 level of significance. e Test the hypothesis that the population proportion of customers who are completely satisfied is less than 0.30 using the p-value approach and a 0.05 level of significance. b. Test the hypothesis that the population proportion of customers who are completely satisfied is different from 0.24 using the p-value approach and a 0.05 level of significance. C.

Answer 1

b)

Ho :   p =    0.22                  
H1 :   p >   0.22       (Right tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   78                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.2600                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0239                  
Z Test Statistic = ( p̂-p)/SE = (   0.2600   -   0.22   ) /   0.0239   =   1.6725
                          
critical z value =        1.645 [Excel function =NORMSINV(α)              
                          
Decision: test stat > 1.645 , reject null hypothesis                       
There is enough evidence that   the population proportion of customers who are completely satisfied is greater than 0.22

e)

Ho :   p =    0.3                  
H1 :   p <   0.3       (Left tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   78                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.2600                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0265                  
Z Test Statistic = ( p̂-p)/SE = (   0.2600   -   0.3   ) /   0.0265   =   -1.5119
                          
  
p-Value   =   0.0653   [excel function =NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis                       
There is not enough evidence that the population proportion of customers who are completely satisfied is less than 0.30

b)

Ho :   p =    0.24                  
H1 :   p ╪   0.24       (Two tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   78                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.2600                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0247                  
Z Test Statistic = ( p̂-p)/SE = (   0.2600   -   0.24   ) /   0.0247   =   0.8111
                          
  
p-Value   =   0.4173   [excel formula =2*NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis                       
There is not enough evidence that  the population proportion of customers who are completely satisfied is different from 0.24