Students in a representative sample of 65 first-year students selected from a large university in England participated in a study of academic procrastination (“Study Goals and Procrastination Tendencies a Different Stages of the Undergraduate Degree,” Studies in Higher Education [2016]: 2028–2043). Each student in the sample completed the Tuckman Procrastination Scale, which measures procrastination tendencies. Scores on this scale can range from 16 to 64, with scores over 40 indicating higher levels of procrastination. For the 65 first-year students in this study, the mean score on the procrastination scale was 37.0 and the standard deviation was 6.44.

a. Construct a 95% confidence interval estimate of m, the mean procrastination scale for first-year students at this college.

b. Based on your interval, is 40 a plausible value for the population mean score? What does this imply about the population of first-year students?