Question

Nick decided to test if there was an association between students' class level and their food preference. He took a random sample of 245 students from his statistic class and found the following data. He plans to conduct a x2 test of independence. Use 3 decimal places where appropriate. Pizza Tacos Sandwich Salad Freshmen 23 18 7 5 Sophomores 19 25 10 12 Juniors 27 22 8. 8 Seniors 24 16 14 7 (a) Assuming that class year and food preference are independent, what is the expected count for the (Sophomore, Tacos) cell? (b) Given a test statistic of 8.176, what is the p-value for Nick's test?

Answer 1

The expected count for (sophomore, Tacos) is computed here as:

E(Sophomore, Tacos) = n(Sophomore) n(Tacos) / n(Total)

= (19 + 25 + 10 + 12)*(18 + 25 + 22 + 16) / 245

= 66*81 / 245

= 21.8204

Therefore 21.8204 is the expected count here.

b) Degrees of freedom here is computed as:
Df = (num of columns - 1)(num of rows - 1) = (4 - 1)(4 - 1) = 9

Therefore the p-value here is computed from chi square distribution tables as:

p= P(X3 > 8.176) = 0.5165

Therefore 0.5165 is the required p-value here.