Exhibit 19-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
-Refer to Exhibit 19-2. The test statistic based on the number of students who preferred to get out early equals
A)1.825
B)0.67
C)0.82
D)3.65

Question

Quizplus · Accepted Answer

To find the test statistic, we need to perform a chi-squared test using the following contingency table:

Break	E. Early	No Pref.
    Observed     40	       80	       30
    Expected	50	       50	       50

The expected counts are all equal because we're testing for independence between the variables. The formula for the chi-squared test statistic is:

χ² = Σ (Observed - Expected)² / Expected

Plugging in the values from the contingency table, we get:

χ² = [(40-50)²/50] + [(80-50)²/50] + [(30-50)²/50] = 3.65

Using a chi-squared distribution table with 2 degrees of freedom (since there are 3 categories), we can see that the critical value for a significance level of 0.05 is 5.99. Since our test statistic (3.65) is less than the critical value, we fail to reject the null hypothesis of independence and conclude that there is not enough evidence to suggest a difference in students' preferences.

Exhibit 19-2 Students in Statistics Classes Were Asked Whether They Preferred a Preferred