Question

Chapter Exercise 9-86 A sample of 103 mortgages approved during the current year showed that 45 were issued to a single-earner family or individual. The historical percentage is 37 percent. At the .05 level of significance in a right-tailed test, has the percentage of single-earner or individual mortgages risen? (a-1) H0: π ≤ .37 versus H1: π > .37. Choose the right option. Reject H0 if zcalc > 1.645 Reject H0 if zcalc < 1.645 a b (a-2) Calculate the test statistic. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.) Test statistic 1.4000 (a-3) The null hypothesis should be rejected. True False (b) Is this a close decision? Yes No (c) State any assumptions that are required. n π < 10 and n(1 − π ) > 10 n π < 10 and n(1 − π ) < 10 n π > 10 and n(1 − π ) > 10 n π > 10 and n(1 − π ) < 10 a b c d

Answer 1

Ho :   p =    0.37  
H1 :   p >   0.37   (Right tail test)
          
Level of Significance,   α =    0.05  
Number of Items of Interest,   x =   45  
Sample Size,   n =    103  
          
Sample Proportion ,    p̂ = x/n =    0.4369  
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0476  
Z Test Statistic = ( p̂-p)/SE =    (0.4369-0.37)/0.0476=   1.41  
          
critical z value =        1.645   [Excel function =NORMSINV(α)
          
p-Value   =   0.0798   [Excel function =NORMSDIST(-z)
Decision:   p value>α ,do not reject null hypothesis       

n π > 10 and n(1 − π ) > 10

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