Consider a multinomial experiment with n = 260 and k = 3. The null hypothesis to

Question

Consider a multinomial experiment with n = 260 and k = 3. The null hypothesis to be tested is H_0: p_1 = 0.60, P_2 = 0.25, P_3 = 0.15. The observed frequencies resulting from the experiment are (Use Table 3): Choose the appropriate alternative hypothesis. n/r Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) chi^2 df n/r Calculate the critical value at the 5% significance level. (Round your answer to 3 decimal places.) chi^2 s,df n/r What is the conclusion to the hypothesis test? n/r

Explanation / Answer

a)

Ho: p1 = 0.60, p2 = 0.25, p3 = 0.15.
Ha: The distribution is not p1 = 0.60, p2 = 0.25, p3 = 0.15.

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b-1.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
163   156   0.314102564  
61   65   0.246153846  
36   39   0.230769231  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    0.791025641   [ANSWER, TEST STATISTIC]

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b-2.  
          
As df = a - 1,           
          
a =    3      
df = a - 1 =    2      
          
          
Hence, the p value is, by table,          
          
P > 0.20

[The more exact P value is 0.673334651].

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c.

As P > 0.05, we fail to reject Ho.

There is no significant evidence that the distribution is not p1 = 0.60, p2 = 0.25, p3 = 0.15.
  
  

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