Medical professionals at a student health center are trying to alert the undergr
ID: 3173837 • Letter: M
Question
Medical professionals at a student health center are trying to alert the undergraduate population about the importance of getting sufficient sleep and the role this plays in their academic performance. The health center staff would like to estimate the true average amount of sleep that the undergraduate students are receiving and construct a 95% confidence interval for this estimate. Furthermore, in order to be useful, the interval can be no more than 2.4 hours wide. Table 1 reports the results from a pilot test that measured the amount of sleep obtained in a random sampling of undergraduate students. Use the standard deviation from this pilot study as your estimate for the population standard deviation.
Table 1: Descriptive statistics for the sleep study
Variable n mean Std.Dev SEmean
Hours of sleep 15 8.5 4.00 1.03
Based on the student health department's criteria, the number of students that should be selected is:
Explanation / Answer
population's standard deviation = sqrt(n)*standard deviation = 4*8.5 = 34
95% confidence interval means 2 times standard deviation < 2.4 hours
=>2*34/sqrt(n) <2.4
=>sqrt(n) > 68/2.4 =28.33
=> n >28.33^2 = 802.5 ~803
Hence the number of students that should be selected is 803 to meet the health department's criteria