Question 4

Due to the outbreak of COVID-19, universities around the world switched to online teaching mainly via Zoom. A researcher in SUSS was interested to know whether the grades of students taking courses via Zoom were different from those taking courses face-to-face in the past. He managed to get the scores of students taking the course face-to-face in 2018. The scores of students taking the same course from 2021 via Zoom were also collected and the raw data are shown in Table Q4. The historical average for this course was 67.5.

⦁ (a)  Find the 95% confidence interval for the SUSS’s class of 2021 for the course. Explain if there is any evidence to suggest that the scores of SUSS’s class of 2021 are similar to the historical average of 67.5.

⦁ (b)  Compute the 95% confidence interval for the SUSS’s class of 2018 exam scores. Compare the two confidence intervals and infer if there is evidence to suggest that the scores of 2021 were lower than those of 2018. Has the outbreak of Covid-19 and the switch to online learning led to a lowering of exam scores?

⦁ (c)  Generate a 95% two-sample confidence interval and test definitively whether the two data sets are statistically different.