A Biology Professor Claims That, on the Average, 20% of Her

Short Answer

A biology professor claims that, on the average, 20% of her students get a grade of A, 30% get a B, 35% get a C, 10% get a D, and 5% get an F. The grades of a random sample of 137 students were recorded. The following table presents the results.
$\begin{array} { c | l l l l l } \text { Grade } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 27 & 37 & 52 & 16 & 5\end{array}$
i). Compute the expected frequencies.
ii). What is the value of $\chi ^ { 2 }$ ?
iii). How many degrees of freedom are there?
iv). Test the hypothesis that the grades follow the distribution claimed by the professor. Use the $\alpha$ = 0.05 level of significance.