An ad agency asks each member of a random sample Please show

An ad agency asks each member of a random sample... Please show your work so I can see how you got your answer.

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 0.05 Program Number 5 4 Total 100 12 12 13 60 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 [ANSWER, VALUE OF CHI^2]
          
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, comparing chi^2 and chi^2(crit) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS. [chi^2 value is not significant]

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B.

We conclude that there is no significant evidence that the viewers have a preference when it comes to tv programs. [ANSWER]