Question

Q1. A local sports bar wanted to determine whether Ohio University students prefer a particular type of food in their establishment. A sample of students responses are reproduced below. Do students prefer a particular type of bar food? Use critical value = 6.58.

Use the numbers below for this question only!

Nachos        Pizza        Chicken Wings        Cheese Sticks

   33               34                    46                          46


What would the expected value for Cheese Sticks be?

Q2. A local sports bar wanted to determine whether Ohio University students prefer a particular type of food in their establishment. A sample of students responses are reproduced below. Do students prefer a particular type of bar food? Use critical value = 6.58.

Use the numbers below for this question only!

Nachos        Pizza        Chicken Wings        Cheese Sticks

   44               40                    42                          43


What is the calculated chi-squared value?

Q.3 Using a critical value of 6.58, was there a significant preference for what students eat in a sports bar based on the obtained chi-square value in Question 2?

Yes

No

Answer 1

Q1:

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)
Nachos	33	0.25	159 * 0.25 = 39.75
Pizza	34	0.25	159 * 0.25 = 39.75
Chicken	46	0.25	159 * 0.25 = 39.75
Cheese sticks	46	0.25	159 * 0.25 = 39.75
Total	159	1.00	159

Expected value for Cheese Sticks = 39.75

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Q2:

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Nachos	44	0.25	169 * 0.25 = 42.25	(44 - 42.25)/42.25 = 0.0725
Pizza	40	0.25	169 * 0.25 = 42.25	(40 - 42.25)/42.25 = 0.1198
Chicken	42	0.25	169 * 0.25 = 42.25	(42 - 42.25)/42.25 = 0.0015
Cheese sticks	43	0.25	169 * 0.25 = 42.25	(43 - 42.25)/42.25 = 0.0133
Total	169	1.00	169	0.2071

Test statistic:

Chi-squared value, χ² = ∑ ((O-E)²/E) = 0.2071

Q3:

χ² = 0.2071 < 6.58, Do not reject the null hypothesis.

No, there is no significant preference for what students eat in a sports bar based on the obtained chi-square.