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.

Homework Answers

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.

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