Question

A large car insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.

Single Policyholders Married Policyholders n1 = 450 n2 = 925 # making claim = 67 # making claim = 93

Using alpha = 0.05, determine whether the claim rates are higher for single male policyholders verses married male policyholders. Solve using the p-value approach only. Which group has the highest insurance claim percentage, single or married policyholders? Why do you think this is the case?

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 >   0          
                  
sample #1   ----->   Single Policyholders
first sample size,     n1=   450          
number of successes, sample 1 =     x1=   67          
proportion success of sample 1 , p̂1=   x1/n1=   0.1489          
                  
sample #2   ----->   Married Policyholders
second sample size,     n2 =    925          
number of successes, sample 2 =     x2 =    93          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.101          
                  
difference in sample proportions, p̂1 - p̂2 =     0.1489   -   0.1005   =   0.0483
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.1164          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0184          
Z-statistic = (p̂1 - p̂2)/SE = (   0.048   /   0.0184   ) =   2.6234
                  
  
p-value =        0.0043 [excel function =NORMSDIST(-z)]      
decision :    p-value<α,Reject null hypothesis               
                  
Conclusion:   There is enough evidence that   claim rates are higher for single male policyholders verses married male policyholders

These could be the case because in case of married it might be the case that Female get the claim instead of male.

Thanks in advance!

revert back for doubt

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