Question

You have been hired to test whether the demand for a product that your client produces varies between two demographic markets – the Urban and Rural markets. As such, in each market, you run a short survey that gauges customers demand for your product and assigns them to one of three categories – (i) High (ii) Medium or (iii) Low.

You survey 80 people in the “Urban” market and find that their demand falls into the following “buckets”

High 42

Medium 20

Low 18

You survey 40 people in the “Rural” market time. Their demand for the product its reflected below.

High 18

Medium 10

Low 12

The Null hypothesis that you are asked to test is that "the demand for the product is INDEPENDENT of the whether the market is Urban or Rural".

For the hypothesis and date above, what is the correct number of degrees of freedom for the Chi-Square distribution?

	30
	3
	5
	9
	12
	50
	6
	1
	32
	4
	70
	10
	2

Assuming that you can tolerate no more than a 5% probability of a Type I error ("p" no larger than 0.05), what is the critical value for the Chi-Square test of the above hypothesis?

	2.706
	7.378
	2.204
	11.143
	5.991
	7.815
	6.251
	1.696
	3.841
	2.833
	5.024

Using the critical values for the 5% and 1% levels of the Chi-Square Distribution from your text, which of the following statements is true

	We can reject the null hypothesis at the 5% level.
	We cannot reject the null hypothesis at the 5% or 1% level
	We can reject the null hypothesis at both the 5% and the 1% levels.
	We can reject the null hypothesis at the 1% level.

Answer 1

degree of freedom(df) =(rows-1)*(columns-1)=

2

2)

for 2 df and 0.05 level , critical value       χ2=

5.991

3)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	urban	Rural	Total
	high	40.000	20.000	60
	medium	20.000	10.000	30
	low	20.000	10.000	30
	total	80	40	120
chi square    χ2	=(Oi-Ei)2/Ei	urban	Rural	Total
	high	0.100	0.200	0.3000
	medium	0.000	0.0000	0.0000
	low	0.200	0.4000	0.6000
	total	0.3000	0.6000	0.900
test statistic X2 =		0.900

sicne test statistic <critical value at 5% level:

We cannot reject the null hypothesis at the 5% or 1% level