Question

Suppose that a response can fall into one of k = 5 categories with probabilities p1, p2, , p5 and that n = 300 responses produced these category counts.

Category 1 2 3 4 5

Observed Count 45 65 72 53 65

(a) Are the five categories equally likely to occur? How would you test this hypothesis?

(b) If you were to test this hypothesis using the chi-square statistic, how many degrees of freedom would the test have?

(c) Find the critical value of χ² that defines the rejection region with α = 0.05. (Round your answer to three decimal places.)

(d) Calculate the observed value of the test statistic.

(e) Conduct the test and state your conclusions.

Answer 1

a)we will apply chi square goodness of fit test if frequency appear in uniform manner in each category

b)

degree of freedom =categories-1=

4

c)

for 4 df and 0.05 level of signifcance critical region       χ2=

9.488

d)

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.200	45	60.00	-1.94	3.750
2	0.200	65	60.00	0.65	0.417
3	0.200	72	60.00	1.55	2.400
4	0.200	53	60.00	-0.90	0.817
5	0.200	65	60.00	0.65	0.417
total	1.000	300	300		7.800

observed value of the test statistic =7.800

e)

as test statistic is not higher than crtiical value we can not reject null hypothesis

we do not have evidence to conclude that frequency does not appear in uniform manner in each category