AP Statistics Midterm Review Project
Name: _______________________________
For all of the questions below, show all work, all graphs, all calculator
input and anything else you do. Use STATCRUNCH or EXCEL to generate
your data and create the graphs.
Below you will find the most recent Math and English 8th Grade NJ ASK
scores for 26 Verona students—13 male and 13 female. One or two of
the digits in some of the numbers have been left blank. The blanks are
to be filled in with digits from your own Student ID Number. For example,
if your Student ID Number is 171515, Student #1’s math score becomes
117; Student #2’s reading score becomes 316. Etc. The first blank is your
first digit, second blank = your second digit, third blank = your third digit,
and so on until you run out of digits, then start over with your first digit.
All numbers are three digit numbers.
Once you have filled in the table use your data to answer the questions in the packet.
Student
Reading
ID #
Gender Score
Math
Score
Student
Reading
ID #
Gender Score
Math
Score
1
Male
298
1__ __
14
Female
275
225
2
Female
3__6
200
15
Male
294
18__
3
Male
289
25__
16
Male
32__
286
4
Male
316
225
17
Female
312
2__ __
5
Male
243
200
18
Male
26__
125
6
Female
298
1__ __
19
Female
294
200
7
Female
294
14_
20
Female
294
264
8
Male
30__
22__
21
Male
330
16__
9
Male
30__
270
22
Female
28__
275
10
Male
334
156
23
Female
289
141
11
Male
280
16__
24
Female
25__
141
12
Female
31__
191
25
Female
290
225
13
Male
230
225
26
Female
225
280
A passing score on the Math test is a 242, while for the Reading test a 300 is required.
Chapter 1: Exploring Data
1.
What are the individuals in this set of data?
2. Describe the three variables completely.
3. Create a bar chart of the reading and math scores by gender. Explain what the graph says about the pass
rates for males and females.
4. Create a Two-Way Table of Gender vs. Math Pass & Fail rates. Use the table to compare pass/fail rates by
gender.
5. Create a Two-Way Table of Gender vs. Reading Pass & Fail rates. Use the table to compare pass/fail rates by
gender.
6. Create two parallel dot plots comparing Math scores vs. Reading scores. Compare the distributions (SOCS)
based on the dotplots.
7. Create back-to back stemplot comparing Math scores and Reading scores. Compare the distributions (SOCS)
based on the stemplots.
8. Create two histograms showing the distribution of Math and Reading scores.
9. Find the mean, median, IQR, 5-Number Summary and standard deviation for two distributions—all Math
scores and all Reading scores. Compare the data for Math and Reading. Identify any outliers in each
distribution.
Chapter 2: Modeling Distributions of Data
10. Create two Cumulative Relative Frequency Tables—one for all Math scores and another for all Reading
scores. Use appropriate bin/class widths.
11. Graph the Math and Reading scores on the same Cumulative Relative Frequency Chart. Mark on the chart
the 25th, 50th and 75th percentiles for each distribution. Use these points to compare the distributions in a
few sentences.
12. Find the z-scores for the Math and Reading scores at the 25th, 50th and 75th percentiles. Use your raw data—
not the values estimated from the graph—to find the actual scores.
13. A passing score on the Math test is a 242, while for the Reading test a 300 is required. What are the
percentiles for these scores and what are their z-scores.
14. The Verona Superintendent of Schools wants to convert the scores to a more meaningful scale so that
parents can understand the results better. To do this, he divides each score by 10 and then adds 60 thinking
that this will convert the cores to a 0-100% scale. What are the new measures of center (mean and median)
and measures of spread (IQR and standard deviation) for each distribution?
15. We want to determine if the Math and Reading scores are Normally distributed. To determine if this is true
please do the following for each distribution:
a.
b.
c.
d.
e.
Compare the mean and the median for each distribution.
Construct histograms with a normal curve overlay for the Math and Reading Distributions.
Determine how closely the data follow the 68-95-99.7% rule.
Construct a Normal probability plot.
Make a determination based on the results above as to whether or not the distributions are
approximately Normal.
16. After analyzing 3 years’ worth of data, we have calculated the average math score to be 229 with a standard
deviation of 21 or N(229, 21). Use this information to answer the following questions:
a. If John Doe scored a 187, how many standard deviations below the mean was he?
b. If Jane Doe scored a 282, what was her z-score?
c. What percent of students score above a 290?
d. What percent of students score below a 260?
e. What percent of students score between 180 and 276?
f. What score would be in the top 15% of all test takers?
Chapter 3: Describing Relationships
17. Construct a scatterplot of English scores vs. Math scores. Is there an association between the English and
Math scores? Is there a correlation? Provide all graphs including residual plots, equations, r and r2 values.
Correctly describe the relationship (DOFS). Determine if there are any outliers or influential points. If so,
remove them from the data set to determine their effect on the relationship between the scores. Describe
the slope and y-intercept in context and explain why or why not this entire question was appropriate.
Chapter 4: Designing Studies
18. The school has been given a huge multiyear grant and we essentially have unlimited funds to help remediate
and improve our math scores. One of the requirements for the grant is to have an experiment to decide the
best method of remediation. Design a scientifically valid experiment to determine if Program A or Program
B. Program A includes doubling math class time each day while Program B includes individualized online
learning components.
a. Be sure to identify levels, factors and treatments and the method of selecting students for each program
b. A diagram and short paragraph explanation is required.
c. Based on the Male and Female Math and Reading scores, should blocking be used? Why or why not?
19. It is determined that the design created above will be too costly and the administration decides to survey
the school to determine how the students want the remediation. Design a survey using each of the
following methods:
a.
b.
c.
d.
e.
f.
Simple Random Sample
Systematic
Cluster
Stratified
Convenience
Voluntary Response
Your population is all of the students and teachers at HBW—about 500 students and 50 teachers.
20. Pick one of the survey methods above for each of the biases below, and explain fully how you reduced the
bias inherent in each survey method.
a. Undercoverage
b. Response
c. Nonresponse
Chapter 5: Probability: What are the Chances?
21. The administration was convinced by Mr. Forte that a survey would not be the best way and they asked you
to run three separate simulations to see how effective the methods will be. If a class has 15 students in it,
and the method has a 45% chance of being effective, run 20 trials to see what the outcomes would be—
what is the expected distribution of passing rates bases on the simulations. Explain fully how you completed
the simulations using your calculator, a random number table and one other method (dice, cards, magician’s
hat, etc.) Show your results graphically in a dotplot.
22. Calculate the probabilities of passing the math and English exams. Show all work.
23. Create a Venn Diagram showing the relationship between students who passed one or both of the exams.
Use the diagram to answer the following questions:
a.
b.
c.
d.
What is the probability a student selected at random of passing the math or English exams?
What is the probability of passing both exams?
What is the probability that a randomly selected student failed both exams?
Given that you know that a student has passed the English exam, what is the probability that he also
passes the Math exam?
e. Given that you know that a student has passed the Math exam, what is the probability that he also
passes the English exam?
f. Are passing the Math and English exams independent of each other?
g. Are passing the two exams mutually exclusive?
AP Statistics
Mid-Term Exam Review Project
This project is meant to help you prepare for the AP Statistics Mid-Term Exam that will take place on or
about Friday, January 24, 2014.
The deadline for submitting the project is Friday, January 17th. Late work will receive zero credit.
A copy of this project is on my VHS web site and it must be used to do the work.
All answers should be typed or copied from STATCRUNCH or EXCEL. Handwritten responses need to be kept
to a minimum and should only involve numbers or calculations that are too difficult to type.
This is an individual project. You may not work with any other student. You can ask me for help at any time
or you use your book or the internet provided that answers/solutions to identical/similar problems are not
referenced or submitted as your own work.
The project will count for the equivalent of three test grades and be part of your 2nd marking period grade.
“On my honor, I have neither given nor received any unauthorized aid on this project.
Signed: ______________________________________________________________
Name: ______________________________________________________________