Exhibit 11-5
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 11-5. The calculated value for the test statistic equals
A)0.5444
B)300
C)1.6615
D)6.6615

Question

Exhibit 11-5
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 11-5. 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 the last school year and this school year, we can use a chi-square goodness-of-fit test. The expected frequencies for each classification can be calculated by multiplying the total sample size (300) by the proportion of each classification from last year (0.3 for freshmen, 0.24 for sophomores, 0.26 for juniors, and 0.2 for seniors). 
Using a calculator or software, we can calculate the chi-square test statistic as:

χ2 = Σ(Oi - Ei)2 / Ei
where Oi is the observed frequency for each classification and Ei is the expected frequency for each classification.

Plugging in the values from the table and the calculated expected frequencies, we get:

χ2 = [(82-90)2/90] + [(71-72)2/72] + [(72-78)2/78] + [(75-60)2/60] 
= 1.6615

The calculated value for the test statistic is 1.6615.
Therefore, the answer is C.

Exhibit 11-5 Last School Year, the Student Body of a Local University