Question

A restaurant chain that has 3 locations in Portland is trying to determine which of their 3 locations they should keep open on New Year’s Eve. They survey a random sample of customers at each location and ask each whether or not they plan on going out to eat on New Year’s Eve. The results are below. Run a test for independence to decide if the proportion of customers that will go out to eat on New Year’s Eve is dependent on location. Use α=0.05.

	NW Location	NE Location	SE Location
Will Go Out	66	40	45
Won’t Go Out	20	25	20

Can it be concluded that the choice to go out on New Year's Eve is dependent on restaurant location?

• A.

  No, it cannot be concluded that the choice to go out on New Year's Eve is dependent on restaurant location because the p-value = 0.8706

• B.

  Yes, it can be concluded that the choice to go out on New Year's Eve is dependent on restaurant location because the p-value = 0.8706

• C.

  Yes, it can be concluded that the choice to go out on New Year's Eve is dependent on restaurant location because the p-value = 0.1294.

• D.

  No, it cannot be concluded that the choice to go out on New Year's Eve is dependent on restaurant location because the p-value = 0.1294.

Answer 1

This is a test for independent between two categorical variables. So we will use chi-square dist.

Observed	NW Location	NE Location	SE Location	Total
Will Go Out	66	40	45	151
Won’t Go Out	20	25	20	65
Total	86	65	65	216
Expected	NW Location	NE Location	SE Location	Total
Will Go Out	60.12037	45.43981	45.43981	151
Won’t Go Out	25.87963	19.56019	19.56019	65
Total	86	65	65	216

Expected Value of a cell =R total * c total / overall total ...................... r = no. of rows and c = no. of columns

	NW Location	NE Location	SE Location
Will Go Out	0.57501	0.65123	0.00426
Won’t Go Out	1.33580	1.51285	0.00989

Chi -square test STat =

Test Stat = 4.08904

c. df = (r -1) * (c -1) ...................... r = no. of rows and c = no. of columns

= 1* 2

df = 2

p - value = P( > T.S.)

= P( > 4.09) ....using chi -square dist tables

p-value = 0.129

Null hypo: The choice to go out on New Year's Eve is not dependent on restaurant location

Alternative hypo: The choice to go out on New Year's Eve is dependent on restaurant location

Since p-value > 0.05

We do not reject the null hypothesis

The choice and location are independent.

D.

No, it cannot be concluded that the choice to go out on New Year's Eve is dependent on restaurant location because the p-value = 0.1294.