A researcher in California is investigating how gender is related to school discipline.

She is studying a random sample of 500 students from a large high school in California with more than 5,000 students. In her sample, 83% of the students who have been suspended from school are boys. This is higher than for the state of California as a whole, where 79% of students who have been suspended are boys, according to the Department of Education’s Civil Rights Data Collection. After learning this, the principal of the school wants to know:

Does this school really have a larger gender imbalance in its suspension rates than in California as a whole? The principal strongly believes that there is no reason to suspect that her high school is any harsher on boys than any other school in the state.

a. Conduct a hypothesis test at the .01 alpha-level. Show all of the steps. In setting up the null and alternative hypotheses, keep in mind that the principal does not believe her school punishes boys more harshly than other schools do. Explain whether you can reject the null hypothesis.

b. How would you explain the p-value from the hypothesis test to the principal, who is unfamiliar with statistical analysis?

c. The principal reports to her staff that “there is only a 2.6% chance that the gender composition of the suspended population at their school is the same as it is across the state.” Is this correct? Explain your answer.