Students in statistics classes were asked whether they preferred a 10-minute break or to allow them go out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred going out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences. The test statistic based on the number of students who preferred going out early equals (Use the continuity correction factor.)
A) 1.83.
B) .67.
C) .82.
D) 3.56.

Question

Quizplus · Accepted Answer

We can use the chi-squared test for goodness of fit to test whether there is a difference in students' preferences. The null hypothesis is that the proportions of students who prefer a break, prefer going out early, and have no preference are equal to the expected proportions. The expected proportions are calculated as follows:

Expected proportion of students who prefer a break = (150-30)/150 = 0.8
Expected proportion of students who prefer going out early = (150-30)/150 = 0.8
Expected proportion of students who have no preference = 30/150 = 0.2

The expected number of students in each category is then calculated by multiplying the expected proportion by the total sample size. The observed and expected values are:

Observed     Expected     (O-E)^2/E
Prefer break        40                  120/3          20
Prefer go out     80                  120/3          6.67
No preference   30                  30                  0
Total                      150                150

The test statistic is the sum of the (O-E)^2/E values, which is 20 + 6.67 + 0 = 26.67. The degrees of freedom for the chi-squared test for goodness of fit is (number of categories - 1) = 3-1 = 2. Using a chi-squared distribution table or calculator, the critical value at alpha=0.05 with 2 degrees of freedom is 5.99. Since our test statistic (26.67) is larger than the critical value (5.99), we reject the null hypothesis and conclude that there is a difference in students' preferences. The answer is D (3.56) with continuity correction factor.

Students in Statistics Classes Were Asked Whether They Preferred a 10-Minute