Question

You are conducting a Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

H0H0 : pA=0.15pA=0.15; pB=0.3pB=0.3; pC=0.15pC=0.15; pD=0.4pD=0.4

Give all answers as decimals rounded to 3 places after the decimal point, if necessary.

Complete the table:

Category	Observed Frequency	Expected Frequency
A	29
B	56
C	29
D	50

What is the chi-square test-statistic for this data?
Test Statistic: χ2=χ2=

For a significance of level alpha = 0.005, what is the chi-square critical value?

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

Category	Observed Frequency	Expected Frequency
A	14
B	25
C	20
D	18
E	19

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.)
χ2=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 =

Critical Value: χ2=χ2=

Answer 1

		observed	Expected
category		Oi	Ei=total*p
A		29.00	24.60
B		56.00	49.20
C		29.00	24.60
D		50.00	65.60

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.1500	29.00	24.60	0.89	0.787
B	0.3000	56.00	49.20	0.97	0.940
C	0.1500	29.00	24.60	0.89	0.787
D	0.4000	50.00	65.60	-1.93	3.710
total	1.000	164	164		6.2236
test statistic X2 =		6.224

for 0.005 level and 3 df :crtiical value X2 =

12.838

2)

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.2000	14.00	19.20	-1.19	1.408
B	0.2000	25.00	19.20	1.32	1.752
C	0.2000	20.00	19.20	0.18	0.033
D	0.2000	18.00	19.20	-0.27	0.075
E	0.2000	19.00	19.20	-0.05	0.002
total	1.000	96	96		3.2708
test statistic X2 =		3.271

degree of freedom =categories-1=

4

for 0.05 level and 4 df :crtiical value X2 =

9.488