You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.
Category  Observed Frequency 
Expected Frequency 


A  11  
B  20  
C  20  
D  7  
E  12 
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chisquare teststatistic for this data? (Report answer
accurate to three decimal places, and remember to use the unrounded
Pearson residuals in your calculations.)
χ2=
What are the degrees of freedom for this test?
d.f.=
What is the pvalue for this sample? (Report answer accurate to
four decimal places.)
pvalue =
Is the pvalue less than αα?
This test statistic leads to a decision to...
As such, the final conclusion is that...
observed  expected  O  E  (O  E)² / E 
11  14.000  3.000  0.643 
20  14.000  6.000  2.571 
20  14.000  6.000  2.571 
7  14.000  7.000  3.500 
12  14.000  2.000  0.286 
70  70.000  0.000  9.571 
What is the chisquare teststatistic for this data? (Report
answer accurate to three decimal places, and remember to use the
unrounded Pearson residuals in your calculations.)
χ2= 9.571
What are the degrees of freedom for this test?
d.f.=4
What is the pvalue for this sample? (Report answer accurate to
four decimal places.)
pvalue = 0.0483
Is the pvalue less than αα?
no
This test statistic leads to a decision to...
fail to reject the null
As such, the final conclusion is that...
There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
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