Question

Can someone please help me with this question? 13.1

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

Category	Observed Frequency	Expected Frequency
A	11
B	9
C	22
D	7
E	11

Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.

b. 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.)
χ2=___________

c. What are the degrees of freedom for this test?
d.f.= ____________

d. What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = _________________

e. The p-value is...

• less than (or equal to) αα
• greater than αα

f. This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• accept the alternative

g. 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.

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 60 4 11.333333 0.0231

Hence,

a) The complete table will be:

Category	Observed Frequency	Expected Frequency
A	11	12
B	9	12
C	22	12
D	7	12
E	11	12

b) χ2 = 11.333

c) d.f. = 4

d) p - Value = 0.0231

e) less than (or equal to) α

f) Reject the null

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