Question

# You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5...

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.

 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.

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