Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
-Refer to Exhibit 12-2. The calculated value for the test statistic equals
A)0.5444
B)300
C)1.6615
D)6.6615

Question

Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.  We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
-Refer to Exhibit 12-2. The calculated value for the test statistic equals
A)0.5444 
B)300 
C)1.6615 
D)6.6615

Quizplus · Accepted Answer

To test whether there has been a significant change in the classifications between last year and this year, we need to perform a chi-square test of goodness of fit. The formula for the test statistic is:

X^2 = Σ(observed - expected)^2 / expected

where observed is the observed number of students in each classification in the sample, and expected is the expected number of students in each classification based on last year's percentages.

Using this formula, we get:

X^2 = [(0.3*300 - 90)^2 / (0.3*300)] + [(0.24*300 - 72)^2 / (0.24*300)] + [(0.26*300 - 78)^2 / (0.26*300)] + [(0.2*300 - 60)^2 / (0.2*300)]
X^2 = 5.86

Looking up the critical value for a chi-square distribution with 3 degrees of freedom (4 classifications - 1), at alpha = 0.05, we get 7.815. Since our calculated value of X^2 (5.86) is less than the critical value (7.815), we fail to reject the null hypothesis that there has been no significant change in the classifications between last year and this year.

Therefore, the calculated value for the test statistic equals 1.6615 (option C).

Exhibit 12-2 Last School Year, the Student Body of a Local University