Question

AST251H1-F (Life on Other Worlds), which was a summer half course, recently had their final exam. The instructional team conducted a benchmarking session using a random sample of 15 students. The average test score in the sample was 66.5 points out of 125, with a standard deviation of 9.36 points. The course instructor would like to know if the class average for the summer session is lower than the class average for the winter 2020 session, which was 71 points out of 125. How strong is the evidence that the class average for the summer session is lower than the class average for the winter session? Answer with null and research hypotheses in formal notation, a quantitative analysis, an approximate p-value, and 1 - 2 sentences interpreting your finding. Note: Do not use a computer to get the p-value. Use the appropriate table provided in the aid sheets.

Answer 1

As we are testing here whether the mean score is less than the class average of 71 points, therefore this is a lower tailed test for which the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

For n - 1 = 14 degrees of freedom, the p-value is obtained from the t distribution tables as:

p = P(t₁₄ < -1.86) = 0.0420

As the p-value here is 0.0420 < 0.05 which is the general level of significance, therefore the test is significant here at the 5% level of significance. Therefore we have sufficient evidence here that the class average for the summer session is lower than the class average for the winter 2020 session