Question

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

Category	Observed Frequency	Expected Frequency
A	10
B	5
C	21
D	14
E	8

What is the chi-square test-statistic for this data?

χ2=

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 =

Is the P-Value...

• A. less than (or equal to) α
• B. greater than α

This test statistic leads mean we?

• A. fail to reject the null
• B. accept the null
• C. reject the null
• D. accept the alternative

so, the final conclusion is that?

• A. The sample data support the claim that all 5 categories are equally likely to be selected.
• B. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• C. There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• D. There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

Answer 1

The statistical software output for this problem is :

Chi-Square goodness-of-fit results: Observed: Oi Expected: All cells in equal proportion N DF Chi-Square P-value 58 4 13.206897 0.0103 Observed. Expected 10 11.6 5 11.6 21 11.6 14 11.6 8 11.6

Test statistics $\chi^2$ = 13.2069

Degrees of freedom = 4

P-value = 0.0103

P-value is less than (or equal to) α .

C. reject the null

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