You are conducting a multinomial hypothesis test ( = 0.05) for the claim that al

Question

You are conducting a multinomial hypothesis test ( = 0.05) for the claim that all 5 categories are equally likely to be selected.

Complete the table.

Category Observed Frequency Expected Frequency

A    20

B    13

C    21

D    5

E 6

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.) 2 = 2=

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 = The p-value is...

less than (or equal to)

greater than

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.

Explanation / Answer

applying chi square goodness of fit on above:

from abvove :  chi-square test-statistic for this data =17.385

degrees of freedom =categories-1=5-1=4

p-value = 0.0016

The p-value is less than

This test statistic leads to a decision to reject the null

There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E A 1/5 20.000 13.00 3.77 B 1/5 13.000 13.00 0.00 C 1/5 21.000 13.00 4.92 D 1/5 5.000 13.00 4.92 E 1/5 6.000 13.00 3.77 1 65 65 17.385

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