Question

A corporation randomly selects 150 salespeople and finds that​ 66% who have never taken a​ self-improvement course would like such a course. The firm did a similar study 10 years ago in which​ 60% of a random sample of 160 salespeople wanted a​ self-improvement course. The groups are assumed to be independent random samples. Let

pi 1π1

and

pi 2π2

represent the true proportion of workers who would like to attend a​ self-improvement course in the recent study and the past​ study, respectively.

What is the critical value when performing a ​chi-square test on whether the population proportions are different if alpha a ​= 0.05?

Answer 1

Hypothesis:

Ho:The population proportions are same. i.e. P1=P2

V/s

H1:The population proportions are different. i.e. P1P2

We can use Z-test and Chisquare test to testing population proportion. But here you need ChiSquare test then we perform this

Here some information is given,

150 salespeople and finds that​ 66% who have never taken a​ self-improvement course.

60% of a random sample of 160 salespeople wanted a​ self-improvement course.

we know that,

using this formula,

x1= #actually dont take any self improvement course

x2= #who was interested to take self improvement course

			row total
Never taken self improvement	99	51	150
want take self improvement	96	64	160
column total	195	115	310

We compute expected count,

Expected count
			row total
Never taken self improvement	94.3548	55.6451	150
taken self improvement	100.6452	59.3548	160
column total	195	115	310

	(Oi-Ei)^2/Ei
	0.22868877
	0.38776018
	0.21439555
	0.36354066
total	1.19438516

it is calculated value

Critical value for

Here < then we accept Ho and conclude that the population proportions are same.

i.e.P1=P2