Goodness-of-Fit Test · Exercise 24

UCLA conducted a survey of more than 263,000 first-year students from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). 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 men fit the distribution of their expected majors.

\begin{array}{|c|c|c|}\hline \text{Major} & \text{Men - Expected Major} & \text{Men - Actual Major} \\ \hline \text{Arts & Humanities} & \text{11.0%} & \text{600} \\ \hline \text{Biological Sciences} & \text{6.7%} & \text{330} \\ \hline \text{Business} & \text{22.7%} & \text{1130} \\ \hline \text{Education} & \text{5.8%} & \text{305} \\ \hline \text{Engineering} & \text{15.6%} & \text{800} \\ \hline \text{Physical Sciences} & \text{3.6%} & \text{175} \\ \hline \text{Professional} & \text{9.3%} & \text{460} \\ \hline \text{Social Sciences} & \text{7.6%} & \text{370} \\ \hline \text{Technical} & \text{1.8%} & \text{90} \\ \hline \text{Other} & \text{8.2%} & \text{400} \\ \hline \text{Undecided} & \text{6.6%} & \text{340} \\ \hline\end{array}

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §11.2 Goodness-of-Fit Test · Exercise 24