Question

question 9 (essay worth 10 points)
(04 02 mc)
a food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the questions:

	likes hamburgers	does not like hamburgers	total
does not like burritos	95	33
total	134		205

part a: what percentage of the survey respondents liked hamburgers but do not like burritos? show all work. (3 points)
part b: what is the marginal relative frequency of all customers who like hamburgers? show all work. (3 points)
part c: is there an association between liking burritos and liking hamburgers? use ratios of joint and marginal frequencies to support your answer. (4 points)

Explanation:

Step1: Complete the frequency - table

First, find the number of people who like burritos but do not like hamburgers. Since the total number of people who like burritos is 77 and 39 of them like hamburgers, then the number is \(77 - 39=38\).
The total number of people who do not like hamburgers is \(38 + 33=71\).
The completed table is:

	Likes hamburgers	Does not like hamburgers	Total
Does not like burritos	95	33	128
Total	134	71	205

Step2: Calculate the percentage for Part A

The number of people who like hamburgers but do not like burritos is 95. The total number of survey respondents is 205. The percentage is \(\frac{95}{205}\times100\%\approx46.34\%\)

Step3: Calculate the marginal relative frequency for Part B

The marginal relative frequency of all customers who like hamburgers is the number of customers who like hamburgers divided by the total number of customers. So it is \(\frac{134}{205}\approx0.6537\)

Step4: Analyze the association for Part C

The joint - frequency of people who like both burritos and hamburgers is 39. The marginal frequency of people who like burritos is 77 and the marginal frequency of people who like hamburgers is 134.
The ratio of the joint - frequency of people who like both to the marginal frequency of people who like burritos is \(\frac{39}{77}\approx0.5065\)
The ratio of the joint - frequency of people who like both to the marginal frequency of people who like hamburgers is \(\frac{39}{134}\approx0.2910\)
If there was no association, these ratios would be approximately equal to the overall proportion of people who like the other food. Since the ratios are different, there is an association between liking burritos and liking hamburgers.

Answer:

Part A: Approximately \(46.34\%\)
Part B: Approximately \(0.6537\)
Part C: Yes, there is an association between liking burritos and liking hamburgers.