Goodness-of-Fit Test · Exercise 24

UCLA conducted a survey of more than 263,000 college freshmen 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 females and 5,000 graduating males 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 percent because of rounding.

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

\begin{array}{|c|c|c|}\hline \text{Major} & \text{Males—Expected Major} & \text{Males—Actual Major} \\ \hline \text{Arts & Humanities} & \text{11%} & \text{600} \\ \hline \text{Biological Sciences} & \text{6.7%} & \text{330} \\ \hline \text{Business} & \text{22.7%} & \text{1,130} \\ \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, Statistics · §11.2 Goodness-of-Fit Test · Exercise 24