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.At a .05 level of significance, the null hypothesis
A) should not be rejected.
B) should be rejected.
C) was designed wrong.
D) cannot be tested.

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.At a .05 level of significance, the null hypothesis
A) should not be rejected.
B) should be rejected.
C) was designed wrong.
D) cannot be tested.

Quizplus · Accepted Answer

The chi-square test statistic is 2.76, which is less than the critical value of 7.815. Therefore, we fail to reject the null hypothesis and conclude that there has not been a significant change in the classifications between the last school year and this school year.

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 $\begin{array} { l l } \text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$