IMathAS-libretexts

You are conducting a multinomial hypothesis test (

\displaystyle \alpha

= 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category	Observed Frequency	Expected Frequency	Squared Pearson Residual
A	11
B	19
C	7
D	6
E	24

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.)

\displaystyle \chi^{{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) $\displaystyle \alpha$
greater than $\displaystyle \alpha$

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.

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