A biology professor claims that, on the average, $15 \%$ of her students get a grade of $A$, $25 \%$ get a B, $40 \%$ get a C , $10 \%$ get a D, and $10 \%$ get an $\mathrm { F }$. The grades of a random sample of 131 students were recorded. The following table presents the results.
$\begin{array}{c|lllll}
\text { Grade } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 13 & 21 & 73 & 11 & 13
\end{array}$

What is the value of $\chi ^ { 2 }$ ?
A) 14.902
B) 9.488
C) 11.143
D) 16.873

Question

A biology professor claims that, on the average, $15 \%$ of her students get a grade of $A$, $25 \%$ get a B, $40 \%$ get a C , $10 \%$ get a D, and $10 \%$ get an $\mathrm { F }$. The grades of a random sample of 131 students were recorded. The following table presents the results.
$\begin{array}{c|lllll}
\text { Grade } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Observed } & 13 & 21 & 73 & 11 & 13
\end{array}$

What is the value of $\chi ^ { 2 }$ ?
A) 14.902
B) 9.488
C) 11.143
D) 16.873

Quizplus · Accepted Answer

The chi-square statistic is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. The expected frequencies are calculated based on the professor's claims: $E_A = 19.65$, $E_B = 32.75$, $E_C = 52.4$, $E_D = 13.1$, $E_F = 13.1$. Calculating $\chi^2$ gives approximately 14.902.

A Biology Professor Claims That, on the Average 15%15 \%15% Of Her Students Get a Grade Of

A Biology Professor Claims That, on the Average $15 \%$ Of Her Students Get a Grade Of