Question

A research team conducted a survey in which the subjects were adult smokers. Each subject in a sample of 200 was asked to indicate the extent to which he or she agreed with the statement. “I would like to quit smoking”. The results were as follows.

Strongly Agree: 102

Agree: 30

Disagree: 60

Strongly disagree: 8

Can one conclude on the basis of these data that, in the sampled population, opinions are not equally distributed over the four levels of agreement?

(a) State the null and alternative hypotheses.

(b) Please calculate the test statistic by hand and compare it with the critical value to test the hypothesis.

(c) Please find the p-value based on an appropriate distribution table to test the hypothesis.

Answer 1

a)

null hypothesis:Ho: in the sampled population, opinions are equally distributed over the four levels of agreement

alternate hypothesis:Ha: : in the sampled population, opinions are not equally distributed over the four levels of agreement

b)

applying chi square test of goodness of fit:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.250	102	50.00	7.35	54.080
2	0.250	30	50.00	-2.83	8.000
3	0.250	60	50.00	1.41	2.000
4	0.250	8	50.00	-5.94	35.280
total	1.000	200	200		99.360

test statistic=99.360

for 0.05 level and 3 degree of freedom :critical value=

7.815

as critical value is lower than test statistic we reject null hypothesis

c)

p value =0.0000 ; as p value is signifcantly low we reject null hypothesis

and conclude that in the sampled population, opinions are not equally distributed over the four levels of agreement