CLASSIC ADVANCED STATISTICS PROBLEMS
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CLASSIC ADVANCED STATISTICS PROBLEMS
Final “Problem Set” May 2022
#1) READING GROUP COMPARISON
Mrs. Hartley and Mrs. Wilson each teach 4th grade at the same elementary school. Mrs. Hartley used a special on-line reading program with her class this year, while Mrs. Wilson used a much more traditional reading program with her students. At the end of the year, both teachers gave their students the same “RAT Test” (Reading Awareness Test). The results are shown below:
Mrs. Hartley’s Class
STATISTIC
Mrs. Wilson’s Class
35
# of students
33
77.5
Mean
74.5
62
Minimum
44
67
Quartile 1
60
72
Median
72
75
Quartile 3
80
80
Maximum
98
a. Given these two 5-number summaries, use the space above to create parallel boxplots to compare the distribution of scores of the two classes.
b. Describe at least one similarity between two groups.
c. Describe at least one difference between the two groups.
d. Are there any outliers in either of the two groups
#2) JOB APPLICATIONS
The website ZipRecruiter.com allows job seekers to fill out a “personal employment profile” listing their education, employment background, special skills, strengths, weaknesses, and personal and professional goals. The website claims that the time it takes job seekers to completely fill out the personal employment profile varies normally, with a mean of 15 minutes and a standard deviation of 3 minutes.
Answer the following questions:
a. What percentage of job seekers using ZipRecruiter.com take more than 20 minutes to fill out their profile
b. What percentage of job seekers using ZipRecruiter.com take between than 12 and 15 minutes to fill out their profile
c. What percentage of job seekers using ZipRecruiter.com take less than 8 minutes to fill out their profile
#3) MEDICAL RESEARCH
The New England Journal of Medicine (NEJM) conducted a case study in Seattle to check if chest compression alone would result in improve survival rate during CPR (cardiopulmonary resuscitation) in comparison to chest compression plus rescue breathing. The results of the NEJM investigation are summarized below:
Successful intervention
Unsuccessful intervention
Total
Chest compression alone
35
205
240
Full CPR
29
249
278
Total
64
454
518
You have been assigned the task of setting up and carrying out a one-sided, two-proportion hypothesis test to determine if the true percentage of successful interventions due to chest compressions alone is significantly greater than the true percentage of successful interventions due to full CPR.
a. State the null hypothesis (Ho) and the alternate hypothesis (Ha) needed to perform this test
b. Compute the sample proportions of successful interventions for each of the two groups
c. Carry out the complete one-sided, two-proportion hypothesis test. Be sure to clearly state your conclusion within the specific context of this problem.
#4) STUDY PREFERENCES
A group of educational psychologists are investigating differences in attitudes towards studying between students attending college in northern states and students attending college in southern states. As part of their research, the psychologists gathered data from 220 students attending private colleges or universities. These students were asked many questions about their study habits, including “in general, do you prefer to study alone, with one or two other people, or in a larger group ” . Here are some of the data that were collected:
STUDY PREFERENCES OF STUDENTS ENROLLED IN NORTHERN COLLEGES
Study Alone
Study with 1 or 2 others
Study in a larger
group
TOTAL
25
55
40
120
STUDY PREFERENCES OF STUDENTS ENROLLED IN SOUTHERN COLLEGES
Study Alone
Study with 1 or 2 others
Study in a larger
group
TOTAL
40
45
15
100
a. Based on the total number of subjects in this survey (all 220 of the students), what is the proportion who preferred to study alone
b. Construct a 95% confidence interval for PN, the true proportion of students at Northern schools who prefer to study alone.
c. Construct a 95% confidence interval for PS, the true proportion of of students at Southern schools who prefer to study alone.
d. Do these two confidence intervals overlap (Yes/No) What, if anything, does this tell you about differences in attitudes between students Northern and Southern schools
#5) FOOTBALL INJURIES
In the National Football League (NFL), each team must submit a “Personnel Injury Report” 4 days prior to each game. In addition to the names of the players who the team knows will definitely not be able to play due to injury, the report also lists the players who are currently injured and who may possibly be able to play in the game. These “possible” players are divided into three groups: Doubtful, Questionable, and Probable. NFL guidelines state that “doubtful” should mean that there is about a 25% chance a player will play, “questionable” means there is a 50% chance that the player will play.
The table below shows the results of a league-wide Personnel Injury Reports for one week of the 2017 NFL season:
DOUBTFUL
QUESTIONABLE
PROBABLE
Played in the game
4
16
52
Did NOT play in the game
16
20
12
a. Of all the players listed in this table, what percentage actually played in the game
b. If a player listed on this chart was selected at random, what is the probability that his pre- game status was “questionable”
c. If a player listed on this chart was selected at random, what is the probability that he played in the game given that his pre-game status was “questionable”
d. If a player listed on this chart was selected at random, what is the probability that he was listed as “probable” in the game given that he played in the game
#6) GRADING
Students at St. Theodore’s school have a grade point average (GPA) based 12-point scale. An A+ is worth 12 points, and A is worth 11 points, an A- is worth 10 points, and so on (see chart below).
Point Scale to Letter Grade Conversion Chart: St. Theodore’s School
Letter
Grade
A+
A
–
B+
B
–
C+
C
–
D+
D
–
F
Point
Value
12
11
10
9
8
7
6
5
4
3
2
1
0
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