a national business magazine reports that the average age of

a national business magazine reports that the average age of retirement for women executives is 61 with a population standard deviation of 2.5 years. A women\'s rights organization believes that this statistic does not accurately depict the current trend in retirement. To test this, they polled 95 recently retired women executives and found they had an average age of retirement of 61.5. use this information to answer the following questions.

a. Determine the p-value

b. is there evidence to support the organization\'s claim at a %95 confidence level? Give reasons for your answer

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   61  
Ha:    u   =/   61  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    61.5          
uo = hypothesized mean =    61          
n = sample size =    95          
s = standard deviation =    2.5          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.949358869          
              
Also, the p value is, as this is two tailed,              
              
p =    0.051252583   [ANSWER]

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b)

As P > 0.05, we fail to reject Ho.      
              
Thus, there is no significant evidence to support the organization\'s claim that the average age of retirement of 61 does not accurately depict the current trend in retirement. [CONCLUSION]