Question

Assume that half of all undergraduate students who drink coffee report that they prefer espresso-based coffee as compared to drip-coffee. A researcher hypothesizes that students in psychology show different distribution of coffee drinking preferences compared to the general population of undergraduate students. In a random sample of 500 psychology students who drink coffee, 330 reported that they preferred espresso-based coffee drinks.

Given this information, please conduct the appropriate two-tailed hypothesis test (α = .05). State the nulland alternative hypotheses.

Answer 1

Let p be the proportion of students who prefer espresso based coffee as compared to drip coffee.

We have to test, H0: p = 0.5 against H1: p 0.5

The test-statistic is given by, Z = , where, = 330/500 = 0.66, = 0.5, n = 500

Thus, Z = 7.1554

Under H0, Z ~ N(0,1)

The p-value = 2 P(Z > 7.1554) = 0

Since, p-value < level of significance = 0.05, we reject H0. We conclude that the proportion of students who prefer espresso based coffee as compared to drip coffee in psychology in significantly different from general undergraduate students.