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".

Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "HIGH" in the URBAN Market?

Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "LOW" in the RURAL Market?

CALCULATE THE TEST STATISTIC FOR THE NULL HYPOTHESIS ABOVE. Enter that answer as a number with two significant decimal places (such as 8.94 or 2.34 or 213.45)

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

Question 10 options:

	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?

Question 11 options:

	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

Solution:

We are given the below table of information:

	Urban	Rural	Total
High	42	18	60
Medium	20	10	30
Low	18	12	30
Total	80	40	120

Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "HIGH" in the URBAN Market?

Answer: The expected number of people that will answer High in the urban market is:

Under this null hypothesis, what is the EXPECTED NUMBER OF PEOPLE THAT WILL ANSWER "LOW" in the RURAL Market?

Answer: The expected number of people that will answer Low in the Rural market is:

CALCULATE THE TEST STATISTIC FOR THE NULL HYPOTHESIS ABOVE.

Answer: The formula for finding the test statistic is:

Where:

O is the observed frequency

E is the expected frequency.

The expected frequencies are:

Therefore, the test statistic is 0.9

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

Answer:

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?

Answer: The chi-square critical value at 0.05 significance level for degrees of freedom 2 is:

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

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