Students in a representative sample of 67 second-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 67 second-year students in the
study at the university, the sample mean procrastination score was 41.00 and the sample standard
deviation was 6.83.
(a) Construct a 95% confidence interval estimate of π, the population mean procrastination scale for
second-year students at this college. (Enter your answer using interval notation. Round your
numerical values to three decimal places.)
b) How does the confidence interval for the population mean score for second-year students compare to
the confidence interval for first-year students of What does this tell you about the
difference between first-year and second-year students in terms of mean procrastination score?
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(a) To construct a 95% confidence interval estimate of π, the population mean procrastination scale for second-year students at this college, we can use the formula:
Confidence interval = sample mean Β± (critical value) * (sample standard deviation / βsample size)
First, let's find the critical value for a 95% confidence interval. Since the sample size is 67, the degrees of freedom is 67 - 1 = 66. Looking up the critical value in the t-distribution table for a 95% confidence interval with 66 degrees of freedom, we find a value of 2.000.
Plugging in the values, we have:
Confidence interval = 41.00 Β± (2.000) * (6.83 / β67)
= 41.00 Β± 1.762
Rounding to three decimal places, the confidence interval estimate of π is [39.238, 42.762].
(b) We are not given information about the confidence interval for the population mean score for first-year students, so it is not possible to directly compare the two intervals. The confidence intervals would need to be constructed using similar methods and parameters in order to make a valid comparison.
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