Consider a multinomial experiment with n = 276 and k = 4. The null hypothesis to

Question

Consider a multinomial experiment with n = 276 and k = 4. The null hypothesis to be tested is H_0: p_1 = p_2 = p_3 = p_4 = 0.25. The observed frequencies resulting from the experiment are (Use Table 3): a. Choose the appropriate alternative hypothesis. Not all population proportions are equal to 0.25. All population proportions differ from 0.25. b. Calculate the value of the test statistic. c. Calculate the critical value at the 5% significance level. d. What is the conclusion to the hypothesis test? Do not reject H_0 since the value of the test statistic does not exceed the critical value. Do not reject H_0 since the value of the test statistic exceeds the critical value. Reject H_0 since the value of the test statistic does not exceed the critical value.

Explanation / Answer

a)

As the opposite of the null hypothesis,

OPTION A: Not all population proportions are equal to 0.25. [ANSWER]

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b)

We then expect 276/4 = 69 as frequency for all.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
76   69   0.710144928  
46   69   7.666666667  
78   69   1.173913043  
76   69   0.710144928  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    10.26086957   [ANSWER]

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c)  
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      

By table,

chi^2(crit) =    7.815 [ANSWER]

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d)
          
As chi^2 > 7,815, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, OPTION D. [ANSWER, D]

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