Question

Which kind of inference?

For each of the examples below, decide whether it makes more sense to use a hypothesis test or a confidence interval. Also decide on the parameter of interest. If you want, you can also write the null and alternative hypotheses (as relevant) for practice.

1. A statistics professor wants to know what proportion of students use their TA's office hour. She takes a random sample of students from all stats classes and ask each student if they have ever visited their TA's office hour.

Answer 1

The appropriate method depends on the professor's goal: use a hypothesis test to evaluate a specific claim or a confidence interval to estimate the student proportion attending TA's office hours. The parameter of interest is the population proportion (p).

Step-by-step explanation:

The question involves deciding between using a hypothesis test or a confidence interval to make an inference about the proportion of students who use their TA's office hour. When a statistics professor wants to know this proportion based on a sample, the parameter of interest is p, the population proportion of students who visit their TA's office hour.

To practice setting up hypotheses, the null hypothesis (H0) could be that the proportion (p) of students who use the TA's office hour is equal to a hypothesized value (for example, p0 = 0.5, if that is the assumed proportion), and the alternative hypothesis (H1) would be that the proportion is not equal to that value (p ≠ 0.5).

If the professor's focus is on estimating the proportion with a certain level of confidence, a confidence interval would be more appropriate. However, if the intent is to test a specific claim about the proportion, then a hypothesis test would be in order.