Introductory statistics
Midterm – fall 2020
Instructions
- All questions receive the same weight in the midterm grade.
- Read carefully all questions and make sure to answer them rigorously and concisely.
A researcher (Tom) wants to know how many hours per week students from a given school spend playing videogames. To answer this question, he randomly samples 150 students from that school. The following table presents that data.
|
Hours played per week
|
Frequency
|
Relative
frequency
|
Cumulative
relative frequency
|
|
0-2
|
20
|
|
|
|
2-4
|
31
|
|
|
|
|
|
4-6
|
44
|
|
|
6-8
|
22
|
|
|
|
8-10
|
28
|
|
|
|
10-12
|
5
|
|
|
Question 1:
Using the above table, compute the mean. Report the measurement units. (Hint: use the midpoints of each “hours played per week” rows to compute the mean.)
Question 2:
Another researcher (Oliver) samples randomly 150 students from the same school as Tom. The following table presents Oliver’s collected data:
Based on his data, Oliver does not find the same sample mean as Tom. Explain whether that highlights a problem in these researchers’ study. In other words, should we worry that 2 researchers measuring the same variable (hours played per week) using samples from the same school will have different means? What can we say about who is right and who is wrong? (No need to compute and report the sample mean for this question.)
Question 3:
Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
|
# of movies
|
Freq
|
|
0
|
6
|
|
1
|
8
|
|
2
|
7
|
|
3
|
3
|
|
4
|
1
|
Compute the IQR (inter-quartile range, i.e. the difference between the 3rd and first quartile) and the standard deviation (square root of the average squared deviation from the mean). Provide all details of your computation (reporting a number is not sufficient) and report the respective measurement units.
Question 4:
Comparing mean and median from question 3, what do you conclude regarding skewness in this empirical distribution?
Question 5:
Discuss whether the dispersion measures from question 3 are robust to outliers (i.e. not or little affected by outliers), i.e. explain briefly why or why not.
Question 6
Two students, Owen and Austin, from different high schools, wanted to find out who had the highest GPA when compared to his school. Which student had the highest GPA when compared to his school?
|
Student
|
GPA
|
School mean GPA
|
School std. dev.
|
|
Owen
|
3
|
3.2
|
0.6
|
|
Austin
|
82
|
85
|
10
|
Question 7 (probability)
|
|
Right handed
|
Left handed
|
|
Males
|
30
|
25
|
|
Females
|
40
|
5
|
Denote the events M = the subject is male, F = the subject is female, R = the subject is right- handed, L = the subject is left-handed.
7.1 Compute the following probabilities:
a. P(M)
b. P(F)
c. P(R)
d. P(L)
e. P(M AND R)
f. P(M OR R)
g. P(M')
h. P(R|M)
7.2 Are M and R independent?
7.3 Are F and L mutually exclusive?