Question

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 59 type I ovens has a mean repair cost of $71.68, with a standard deviation of $15.08. A sample of 48 type II ovens has a mean repair cost of $66.21, with a standard deviation of $10.25. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   71.68                  
standard deviation of sample 1,   s1 =    15.08                  
size of sample 1,    n1=   59                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   66.21                  
standard deviation of sample 2,   s2 =    10.25                  
size of sample 2,    n2=   48                  
                          
difference in sample means =    x̅1-x̅2 =    71.6800   -   66.2   =   5.47  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    13.1394                  
std error , SE =    Sp*√(1/n1+1/n2) =    2.5540                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   5.4700   -   0   ) /    2.55   =   2.142
                          
Degree of freedom, DF=   n1+n2-2 =    105                  

p-value =        0.017263   [excel function: =T.DIST.RT(t stat,df) ]             
Conclusion:     p-value <α , Reject null hypothesis                     
                          
There is enough evidence to sat that the repair cost for type I ovens is greater than the repair cost for type II ovens

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