In 2018, the city of Ithaca took a census where they asked residents which coffee shop was their favorite: 32% preferred Collegetown Bagels (CTB), 25% preferred Gimme! Coffee, and 43% preferred Ithaca Coffee Company. In 2019, Cornell asked a simple random sample of 300 graduate students to answer the same question. Of the students surveyed, 93 preferred CTB, 94 preferred Gimme! Coffee, and 113 preferred Ithaca Coffee Company. We want to answer the research question: Are the coffee shop preferences of Cornell Graduate Students different from the population of Ithacans? Which null hypothesis is appropriate for the above research question. Here p1, p2, and p3 refer to the probability that a Cornell Graduate Student prefers CTB, Gimme! Coffee, or Ithaca Coffee Company, respectively.

(a) p1 = 0.32, p2 = 0.25, p3 = 0.43

(b) p1 = 0.31, p2 = 0.31, p3 = 0.38

(c) p1 = p2 = p3

(d) None of the above

Continuing with the setup of the previous question suppose we ran the following code to answer

the research question and got the corresponding output.

cornell_students_coffee <- c(93, 94, 113)

ithacans_coffee <- c(.32, .25, .43)

chisq.test(x = cornell_students_coffee,

p = ithacans_coffee)

##

## Chi-squared test for given probabilities

##

## data: cornell_students_coffee

## X-squared = 6.8916, df = 2, p-value = 0.03188

Based on the above output, which conclusion is appropriate?

(a) At the 5% level of significance, we do have sufficient evidence to conclude that the Cornell graduate

students have a different distribution of coffee shop preferences than that given in the 2018 census of

all Ithacans.

(b) At the 5% level of significance, we do have sufficient evidence to conclude that the Cornell graduate

students coffee shop preferences are independent of the coffee shop preferences of Ithacans.

(c) At the 1% level of significance, we do have sufficient evidence to conclude that the Cornell graduate

students have a different distribution of coffee shop preferences than that given in the 2018 census of

all Ithacans.

(d) At the 1% level of significance, we do have sufficient evidence to conclude that the Cornell graduate

students coffee shop preferences are independent of the coffee shop preferences of Ithacans.