You are conducting a multinomial hypothesis test (\alpha= 0.05) for the claim that all 5 categ

adoliremdhp

adoliremdhp

Answered question

2022-03-07

You are conducting a multinomial hypothesis test (α=0.05) for the claim that all 5 categories are equally likely to be selected.
 Category  Observed Frequency  A 25 B 13 C 21 D 8 E 9
What is the chi-square test-statistic for this data?
χ2=

Answer & Explanation

zakulisan337

zakulisan337

Beginner2022-03-08Added 1 answers

Given:
∝=0.05.
k = 5
From the provided data we have the computations as,
 Category  Observed Frequency (Oi) Expected Frequency (Ei)OiEi(OiEi)2/Ei A 2576/5=15.29.86.318421 B 1376/5=15.22.20.318421 C 2176/5=15.25.82.213158 D 876/5=15.27.23.410526 E 976/5=15.26.22.528947 Total 7676014.78947
Thus, the chi-square test statistic for the given data is 14.78947.
The degrees of freedom for this test is k -1 = 5-1 = 4
The p-value for this sample is given by using excel as below:
The p-value is 0.0052.

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