Hypothesis of Interest

Question

Between 2009-2010 all high school classes were taught in person. The mean SAT grades during this period was μ=1100

To understand the impact that online classes have on student learning, 16 students were randomly selected and taught using zoom for one year (no in-person teaching). The average grade for the online course was 950.

It has been calculated that the probability that the average grade in a class of 16 students (taught in person) is less than or equal to 950 is 0.13%. What is the hypothesis of interest and what do the results from the study suggest (at the 5% level)?

(A) H0: µ ≤ 1100 vs HA: µ > 1100, the p-value is 0.13% which suggests that online learning may have a negative impact on learning outcomes

(B) H0: µ ≥ 1100 vs HA: µ < 1100, the p-value is 0.13% which suggests that online learning may have a negative impact on learning outcomes

(C) H0: µ ≥ 1100 vs HA: µ < 1100, the p-value is 99.87% which suggests that online learning may have a positive impact on learning outcomes

(D) The data is not very conclusive on about the impact of online learning

Answer 1

(D) this data is not conclusive on the impact of online learning.

In order to perform a hypothesis test, we must meet several different conditions but namely, a large enough sample size is required in order to apply the central limit theorem. In this example, we want to have a large enough sample of students so we can see the probability of the sample mean being 950 IF the null hypothesis is true (that the population mean is greater than or equal to 1100).

16 students is not enough to apply the central limit theorem, ideally, we want more than 30.