Goodness-of-Fit Test · Exercise 21

UCLA conducted a survey of more than 263,000 first-year students from 385 colleges in a certain year. Suppose a survey of 5,000 graduating women and 5,000 graduating men was done as a follow-up last year to determine what their actual majors were. The results are shown in the tables for and. The second column in each table does not add to 100% because of rounding.

Conduct a goodness-of-fit test to determine if the actual college majors of graduating women fit the distribution of their expected majors.

\begin{array}{|c|c|c|}\hline \text{Major} & \text{Women - expected major} & \text{Women - actual major} \\ \hline \text{Arts & Humanities} & \text{14.0%} & \text{670} \\ \hline \text{Biological Sciences} & \text{8.4%} & \text{410} \\ \hline \text{Business} & \text{13.1%} & \text{685} \\ \hline \text{Education} & \text{13.0%} & \text{650} \\ \hline \text{Engineering} & \text{2.6%} & \text{145} \\ \hline \text{Physical Sciences} & \text{2.6%} & \text{125} \\ \hline \text{Professional} & \text{18.9%} & \text{975} \\ \hline \text{Social Sciences} & \text{13.0%} & \text{605} \\ \hline \text{Technical} & \text{0.4%} & \text{15} \\ \hline \text{Other} & \text{5.8%} & \text{300} \\ \hline \text{Undecided} & \text{8.0%} & \text{420} \\ \hline\end{array}

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Business Statistics 2e · §11.3 Goodness-of-Fit Test · Exercise 21