A study was conducted to determine if there is a difference

A study was conducted to determine if there is a difference between theinvesting preferences of mid-level managers working in the public and privatesectors in New York City. A random sample of 320 public sector employeesand 380 private sector employees was taken. The sampled participants werethen asked about their retirement investment decisions and classified asbeing either “aggressive,” if they invested only in stocks or stock mutualfunds, or “balanced,” if they invested in some combination of stocks, bonds,cash, and other. The following results were found:

Aggressive Balance

Public 164 156

Private 236 144

a. State the hypothesis of interest and conduct the appropriate hypothesis test to determine whether there is a relationship between employment sector and investing preference. Use a level of significance of 0.01.

b. State the conclusion of the test conducted in part a.

c. Calculate the p-value for the hypothesis test conducted in part a.

Solution

a)

Ho: The invesment preferences are independent of the sector.

Ha: The invesment preferences are not independent of the sector.

Doing an Expected Value Chart,          
          
182.8571429   137.1428571  
217.1428571   162.8571429  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    8.358552632      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.01      
          
chi^2(critical) =    6.634896601      

As chi^2 > 6.635897, we REJECT THE NULL HYPOTHESIS.

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b)

Thus, there is significant evidence that the investment preference is not independent of the sector. [CONCLUSION]

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c)

Also, the p value is, as df = 1, using table/technology,          
          
P =    0.003838762   [ANSWER]