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.

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 =  
It may be best to use the =CHIDIST() function in Excel to do this calculation.

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.

Category Observed
Frequency Expected
Frequency Squared
Pearson
Residual A 11 B 10 C 14 D 7 E 23

Explanation / Answer

H0: all 5 categories are not equally likely to be selected.

H1: all 5 categories are equally likely to be selected.'

alpha:5%

Test statistic:

where ei=mean of observed freq=13

chisquare=8.036

Degrees of freedom=(n-1) =5-1=4

P value= 0.09

Conclusion:

P>0.05 we donot reject the Ho.

Hence There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

Oi ei (oi-ei)^2/ei 11 13 0.307692 10 13 0.692308 14 13 0.076923 7 13 2.769231 23 13 7.692308

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