Question

Students in a representative sample of 65 first-year students selected from a large university in England participated in a study of academic procrastination. 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 36.9 and the standard deviation was 6.46. (a) Construct a 95% confidence interval estimate of μ, the mean procrastination scale for first-year students at this college. (Round your answers to three decimal places.) , (b) Based on your interval, is 40 a plausible value for the population mean score? Yes No What does this imply about the population of first-year students? This implies that students at this university never have high levels of procrastination. This implies that on average, students at this university do not have high levels of procrastination. This implies that students at this university sometimes have high levels of procrastination. This implies that on average, students at this university do have high levels of procrastination. This implies that students at this university always have high levels of procrastination.

Answer 1

We are given that for the 65 first-year students in the study at the university, the sample mean procrastination score was 36.9 and the sample standard deviation was 6.46.

so,     = sample mean procrastination score = 36.9

             s = sample standard deviation = 6.46

n = sample of students = 65

μ = population mean estimate

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and

we see that

so we can process by putting values in confidence interval formula as shown below