Question

In: Math

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by...

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is _______.

increase the sample size

gather more data

reject the null hypothesis

fail to reject the null hypothesis

maintain status quo

Solutions

Expert Solution

Null hypothesis          

       
                  
Alternative hypothesis      

           
                  
We have for given example,                  
Population proportion value is =0.25              
x=54   
                  
n=300              
Level of significance =   0.01              
Estimate for sample proportion =54/300=0.18
                  
Z test statistic formula for proportion                  


=-2.8  

P value =0.0024.................by using Z table or Excel =NORMSDIST(-2.8)

P value < 0.01

reject the null hypothesis

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