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. $$\begin{array} { l l }
\text { Freshmen } & 83 \
\text { Sophomores } & 68 \
\text { Juniors } & 85 \
\text { Seniors } & 64
\end{array}$$ 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.The calculated value for the test statistic equals
A) .54.
B) .65.
C) 1.66.
D) 6.66.

Question

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. $$\begin{array} { l l } 
\text { Freshmen } & 83 \
\text { Sophomores } & 68 \
\text { Juniors } & 85 \
\text { Seniors } & 64
\end{array}$$   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.The calculated value for the test statistic equals
A) .54.
B) .65.
C) 1.66.
D) 6.66.

Quizplus · Accepted Answer

The calculated value for the test statistic is 1.66. This is because the chi-square statistic is calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the expected frequencies are 30% of 300 = 90 for freshmen, 24% of 300 = 72 for sophomores, 26% of 300 = 78 for juniors, and 20% of 300 = 60 for seniors. The observed frequencies are 83, 68, 85, and 64, respectively. The chi-square statistic is therefore (83-90)^2/90 + (68-72)^2/72 + (85-78)^2/78 + (64-60)^2/60 = 1.66.

Last School Year, the Student Body of a Local University Freshmen 83 Sophomores 68 Juniors 85 Seniors 64\begin{array} { l l } \text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array} Freshmen Sophomores Juniors Seniors ​83688564​

Last School Year, the Student Body of a Local University $\begin{array} { l l } \text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$