Please show your work stepbystep 50 An ad agency asks each m

Please show your work step-by-step.

50. An ad agency asks each member of a random sample of 60 viewers to indicate which of six television programs he or she prefers. Let a = 0. 05 a) Is the X2 value significant at 5% level of significant? b) Write the conclusion for this question

Solution

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
5   10   2.5  
8   10   0.4  
10   10   0  
12   10   0.4  
12   10   0.4  
13   10   0.9  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.6      
          
As df = a - 1,           
          
a =    6      
df = a - 1 =    5      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    11.07049769      
          
Also, the p value is          
          
p =    0.466616274      
          
Thus, as chi^2 (crit) > chi^2, we   FAIL TO REJECT THE NULL HYPOTHESIS. IT IS NOT SIGNIFICANT AT 5%.
[part a]

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We conclude that there is no signficant evidence to tell that the viewers on the average have a special preference on tv shows. [part b]