Question

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 chi-square test-statistic 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 p-value for this sample? (Report answer accurate to four decimal places.)
p-value =


Is the p-value less than αα?

• yes
• no

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• accept the alternative

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• The sample data support the claim that all 5 categories are equally likely to be selected.
• There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

Answer 1

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 chi-square test-statistic 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 p-value for this sample? (Report answer accurate to four decimal places.)
p-value = 0.0483


Is the p-value 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.