Question

Consider the dataset Getting2NoUS2019.csv collected from the Getting To Know You Survey at the beginning of the semester. The details of this dataset are described in the file Getting2NoUS2019 dataset description. For parts a.–b., we examine the distribution of the zzz.week variable (the number of hours slept per night during the week) for the STAT 3011 students. Use the following codes to load the dataset and obtain the frequency table of the zzz.week variable (there are a total of 361 non-missing responses for this variable):

NoU <- read.csv("http://stat.umn.edu/~wuxxx725/data/Getting2NoUS2019.csv", header = T) attach(NoU) table(zzz.week)

a. What is the probability that a randomly chosen STAT 3011 student sleeps less than 6 hours per day during the week?

b. What is the probability that a randomly chosen STAT 3011 student sleeps 8 hours or more per day during the week?

For parts c.–f., we examine the joint distribution of the international.student variable (whether the student is an international or US student) and the season variable (the student’s favorite season) for the STAT 3011 students. Use the following code to obtain the cross table for the distributions of the international.student and season variables (there are a total of 362 non-missing responses for these variable):
(joint_freq <- table(international.student, season))
And use the following codes to obtain the row and columns totals, respectively:
margin.table(joint_freq, 1) margin.table(joint_freq, 2)

c. What is the probability that a randomly chosen STAT 3011 student’s favorite season is winter?
d. What is the conditional probability that a randomly chosen STAT 3011 student’s favorite season is winter, given that he/she is an international student?


e. Based on your answers to parts c. and d., are the event that a student’s favorite season is winter and the event that he/she is an international student independent? Explain.
f. What is the probability that either a randomly chosen STAT 3011 student’s favorite season is winter or he/she is an international student (or both)?

Answer 1

a)

table(zzz.week)
zzz.week
  3   4   5 5.5   6 6.5   7 7.5   8   9 9.5  10 
  2   4   9   2  68   8 135   6 104  18   1   4 

P(X < 6)

= (2 + 4 + 9 + 2)/361

= 0.04709

b)

P(X > = 8)

= (104 + 18 + 1 + 4)/361

= 0.351800

c)

joint_freq <- table(international.student, season)
joint_freq

                season
international.student Fall Spring Summer Winter
        International   14      9     12      5
        U.S.           114     64    121     23

P(Y = winter) = (5 + 23)/362

= 0.07734

d)

P(winter| international )

= 5/(14 + 9 + 12 +5)

= 0.125