8B In-Class Activity

Question 1

Research studies of college students suggest that sleep deprivation and daytime sleepiness can have negative consequences, including lower grade  point averages, increased risk of academic failure, and impaired mood.[1]To counter sleep deprivation and  daytime sleepiness, individuals are  often encouraged to nap during the  daytime.[2] In fact, some have even  argued for colleges to consider  building napping stations in their  libraries to provide students convenient locations for quick naps.[3]


Credit: iStock/skynesher

  1. How many days in the last week have you had a nap? How likely do you  think it is that a randomly selected classmate has had a nap on a majority of  the days in the last week (i.e., in 4 or more days)?
  2. How do you think the class’s napping habits relate to all college students  across the United States?

Question 2

In the preview assignment, you were asked to respond to the following question: “On  how many of the last 7 days did you take a nap?”

We will use the possible values to this question as the possible values of our  discrete random variable. That is, let’s use “[latex]X[/latex]” to represent the number of days that  included a nap.

Using the data provided by your instructor, complete the “Frequency” column in the  table below.

[latex]X[/latex], Number of  days that

included a nap

 Frequency
0
1
2
3
4
5
6
7
TOTAL:

Question 3

Use your frequency table to address the following questions.

  1. Calculate the probability associated with each value of the random variable,  [latex]X[/latex]. That is, calculate the probability of randomly selecting a classmate who  had 0 days with a nap. Then repeat this for the other possible values of the  random variable. Complete the column “[latex]P(X)[/latex]” in the following table.
    [latex]X[/latex], Number of  days that

    included a nap

    		 [latex]P(X)[/latex],

    The probability of

    randomly selecting an  individual who stated � days with a nap
    0
    1
    2
    3
    4
    5
    6
    7
    SUM:
  2. Explain how your table illustrates all of the essential properties necessary for  a discrete probability distribution.

Question 4

Use the probability distribution you created to address the following questions.

  1. Suppose you randomly selected an individual from the class. What is the probability of selecting someone who has had a nap on only 1 day in the past week, [latex]P(X = 1)[/latex]?
  2. Calculate P(3 days or less), or in other words, [latex]P(X≤ 3)[/latex]. Interpret your result.
  3. Suppose you randomly selected an individual from the class. What is the probability that you select someone who has had a nap on a majority of the days in the past week (i.e., at least 4 days)?

 

Question 5

A large, national survey[4] conducted by the American College Health Association asked college students the same question that you answered prior to class: “On how  many of the last 7 days did you take a nap?” The graph below displays the  probability distribution of the random variable [latex]X[/latex], number of days that included a nap.

  1. Compare and contrast this probability distribution with the one associated  with the class responses. How are they similar? How are they different?
  2. What is the probability of selecting a surveyed college student who has had a  nap on at most 2 days in the last week?
    Put another way, calculate [latex]P(X ≤ 2)[/latex].
  3. Calculate P(At least 4 days), i.e., [latex]P(X ≥ 4)[/latex]. Interpret your result.

 

Question 6

Compare your calculations from Question 4, Part C and Question 5, Part C. When compared to those in the national study, is your statistics class more or less likely to find an individual who has had a nap on at least 4 days in the last week?

 

 

 

  1. Hershner, S. D., & Chervin, R. D. (2014). Causes and consequences of sleepiness among college students. Nature and Science of Sleep, 6, 73–84. https://doi.org/10.2147/NSS.S62907 ↵
  2. Duggan, K. A., McDevitt, E. A., Whitehurst, L. N., & Mednick, S. C. (2018). To nap, perchance to DREAM: A factor analysis of college students' self-reported reasons for napping. Behavioral Sleep Medicine, 16(2), 135–153. https://doi.org/10.1080/15402002.2016.1178115 ↵
  3. Wise, M. J. (2018). Naps and sleep deprivation: Why academic libraries should consider adding nap stations to their services for students. New Review of Academic Librarianship, 24(2), 192–210. https://doi.org/10.1080/13614533.2018.1431948 ↵
  4. American College Health Association-National College Health Assessment. (2020). Undergraduate student reference group data report, Fall 2019. https://www.acha.org/NCHA/ACHA NCHA_Data/Publications_and_Reports/NCHA/Data/Reports_ACHA-NCHAIII.aspx ↵