Final answer:
The college mathematics question involves hypothesis testing to ascertain if less than 40 percent of students at a school fear public speaking, based on a sample of 361 students where 135 reported this fear. A null and an alternative hypothesis are set up and a statistical test like a z-test for proportions is performed to test the claim.
Step-by-step explanation:
The question is regarding the analysis of a hypothesis testing situation in mathematics/statistics. The scenario involves conducting a hypothesis test to determine whether the percentage of students at a school who fear public speaking is less than a previously reported 40 percent.
To perform this hypothesis test, one would start by setting up the null hypothesis (H0) that the percentage of students fearing public speaking at the school is equal to or greater than 40 percent, against the alternative hypothesis (Ha) that the percentage is less than 40 percent. Statistical methods such as a z-test for proportions would then be used to determine if there is sufficient evidence to reject the null hypothesis based on the sample data provided.