Question

Suppose I wanted to know whether a surprise quiz before the midterm improves your midterm score. Suppose I’m teaching two sections of this class, and I decide to test this by setting a surprise quiz for the first section and not for the second section, and then comparing the average scores of the two sections on the midterm. What assumption(s) would need to hold in order for me to estimate the true effect of a surprise quiz on midterm score in this manner? Explain.

Answer 1

As per given problem statement, we need to conduct a hypothesis test for the difference between two means from independent samples. To estimate the true effect of a surprise quiz on midterm score by a hypothesis test (using  two-sample t-test), we need hold below assumptions.

• The sampling method for each sample is simple random sampling. That is the sections are randomly selected from the class.
• The sections (samples) are independent.
• The sampling distribution of  midterm score is approximately normal, which is generally the case if any of the following conditions apply.
  • The population distribution of midterm score is normal.
  • The population data of midterm score are symmetric, unimodal, without  outliers, and the sample size is 15 or less.
  • The population data of midterm score are slightly skewed, unimodal, without outliers, and the sample size is 16 to 40.
  • The sample size of midterm score is greater than 40, without outliers.