Question

A survey of 800 workers indicated that approximately 445 have invested in an IRA. National data suggests that 47​%

of workers invest in IRAs. Test the claim that the number of workers who invest in an IRA is now different than this reported national value. Use α=0.05 and state your conclusion.

​The test statistics is?

The P value is?

What is your conclusion?

Answer 1

Null hypothesis      

               
                      
Alternative hypothesis  

                   
                      
We have for given example,                      
Population proportion value is =0.47                  
x=445                  
                      
n=800                  
Level of significance =   0.05                  
Estimate for sample proportion = \hat{p}=0.55625                  
                      
Z test statistic formula for proportion

  
=4.89                  
                      
P value is 0.000001              
P value is approximately 0

We have sufficient evidence at to say that, the number of workers who invest in an IRA is now different than this reported national value.