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 23

B 24

C 16

D 5

E 17

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=

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...(choose 1)

reject the null

accept the null

fail to reject the null

accept the alternative

As such, the final conclusion is that... (choose1):

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

The statistical software output for this problem is:

Chi-Square goodness-of-fit results:
Observed: Observed
Expected: All cells in equal proportion

Hence,

X2 = 13.529

Df = 4

p - Value = 0.0090

Less than

Reject Null

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

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