"Course RedesignPass rates for Intermediate Algebra at a commu...

Question

"Course RedesignPass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of a community college develop a mastery-based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning mentor for the students. Of the 480 students who enroll in the mastery-based course, 267 pass.

c. Explain why a 0.01 level of significance might be used to test this hypothesis."

c. Explain why a 0.01 level of significance might be used to test this hypothesis."

Accepted Answer

Welcome back, everyone. In this problem, a community health program has a baseline vaccination uptake of 0.45. A new outreach campaign enrolls N equals 640 households and observes 308 households vaccinated. Explain why investigators might select alpha as 0.01 for testing whether the campaign increased uptake. A says the investigators chose alpha equals 0.01 because the sample size is small and a smaller alpha compensates for that. B says it's because the probability of a type 1 error equals alpha and the intervention has low cost, so we want to be conservative. She says it's because policy decisions based on the result are high stakes, so they want to minimize the chance of a false positive by setting the probability of a type 1 error to 0.01, and he says it's because a smaller alpha always leads to smaller confidence intervals which is desirable. No, we're trying to figure out why our investigators would select this alpha value, that is our level of significance to be 0.01 for testing, OK? So let's look at each choice and evaluate it's whether it's true. Let's reason on what the statement is saying. Now the first one, it says that they chose it because the sample size is small and are smaller. Significance level alpha compensates for that. What do we know? Well, we know the rule is that decreasing alpha, OK, decreasing alpha. When N is small, OK. Further reduces the power, OK. Now in our statement, it says that this because the sample size is small and a smaller alpha compensates for that. But this doesn't justify making alpha smaller to compensate because as it said, it further reduces the power. Thus this reasoning is incorrect and A is not the right answer. Let's look at answer choice B. It says it's because the type, the probability of a type 1 error is the level of significance alpha and the intervention has low cost, so we want to be conservative. Now it is true, OK. It is true that. Choosing a smaller alpha reduces a type 1 error because the probability of a type 1 error is equal to alpha. This part is correct. However, when they say that the intervention has a low cost, that contradicts the usual reason for being conservative. We would likely want to be conservative if this is a high stakes decision. So that means this choice would be inconsistent and thus B also could not be the correct answer. Now what about answer Tray? Well, It says here because policy decisions based on the results are high stakes, so they want to minimize the chance of a false positive by setting the probability of a type one error to 0.01. Remember, alpha is 0.01, so similar to B, this probability is equal to our significance level alpha. The rule is that when results inform high stakes policy, selecting alpha to be 0.01 reduces the risk of making a costly false positive decision. So with a large sample N equals 640, a power remains high even at an alpha value of 0.01. So strict evidence can be required without greatly reducing the ability to detect meaningful increases. Therefore, C is the correct answer. We know we're right if we look at answer choice D to see if it is true. D says they chose it because smaller alpha always leads to smaller confidence intervals, which is desirable. That's not necessarily true. A smaller alpha doesn't lead to smaller confidence intervals, but rather wider confidence intervals. So this statement is false. That's how we're sure that C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Level of Significance

Hypothesis Testing

Type I Error and Its Control

Watch next