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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. Hartleys Class

STATISTIC

Mrs. Wilsons 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. Theodores 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