3Q. A salesman paid 12 visits to his area sales manager and noted that he had to wait for 10,15,20,17,11,25,30,27,36,40,5 and 26 minutes, respectively, before being called in hisoffice. The area salesmanagerclaims that the salesmen wishing to meet him do not have to wait for more than 20 minutes before being called in. Using the sign test, verify at 0.05 level of significance the claim made by the area salesmanagerSolution:Step 1 and 2:defining Hypothesis1. Null Hypothesis (H0): Md=20(counter claim)The waiting time for salesman before being called in by the sales Manager is less than 20 minsStep 3: Level of Significance (LOS)=0.05 (right tail)Step4: Calculation of Test StatisticMedian M=20Subtract each of the X values from 20No of Visits by Sales manWaiting time of SalesmanX-20

110-10

215-5

3200

417-3

511-9

625+5

730+10

(827+7

936+16

1040+20

115-15

1226+6

No of + signs =6No of signs = 5No of 0s =1n= no of + and - signs excluding 0n=12-1=11X= No of times a particular + or - sign has occurred less frequentlyCalculated value min (+ signs, - signs) = (6, 5) = 5Step 5:Critical Value for X for n=11 at 0.05 level of significance for one sample test is 2 (from tables).X