Question

Bistro 65 is a chain of Italian restaurants operating in Ohio and Kentucky. Their menu has 4 categories of entrees: Pasta, Steak & Chops, Seafood, and Other (pizzas, sandwiches, etc...) Historical data for the chain shows that 40% of all orders are for Pasta, 10% for Steak & Chops, 20% for Seafood, and 30% for Other. A new Bistro 65 restaurant has just opened in Dayton and the following purchase frequencies were recorded for the first 200 customers:

Pasta	Steak & Chops	Seafood	Other
f: 70	f: 30	f: 50	f: 50

If the null is: , then use the table to calculate the appropriate Test Statistic in order to calculate the correct PValue, rounded off to the second decimal place.

The PValue for this test is: Blank 1. Fill in the blank, read surrounding text. Do NOT enter degrees of freedom. Do NOT enter letters.

Answer 1

Null hypothesis : There is no significant difference between the observed and expected purchase frequency of the orders.

Alternative hypothesis : There is significant difference between the observed and expected purchase frequency of the orders.

Test statistic is given by -

Degrees of freedom = k - 1 = 4 - 1 = 3

Where, k is the number of categories of food.

Oi is the observed frequency of the ith category.

Ei is the expected frequency of the ith category.

Observed frequency (Oi)	Expected frequency (Ei)
70 30 50 50	40% * 200 = 80 10% * 200 = 20 20% * 200 = 40 30% * 200 = 60	1.250 5.000 2.500 1.667
N = 200	N = 200	= 10.417

So, the value of the test statistic will be -

P value =

= Area under the chi square curve with 3 degrees of freedom on the right side of chi square = 10.417

= 0.0153

~ 0.02

It can be calculated using the formula =CHIDIST(10.417,3) in Excel.