Mrs. Daniel- AP Stats “Create Your Own FRQs” Project You need to create three of your own Free Response Questions (FRQs). Each FRQ must be modeled after

an existing CollegeBoard FRQ and have a worked out solutions.

Attached to the directions are a sample “Create Your Own FRQ” modeled after FRQ 2011 #1 and a

sample solution to the newly created FRQ. All FRQs must be typed. Solutions maybe handwritten. The

typed FRQs need to be submitted via Dropbox

(https://www.dropbox.com/request/RGmEiYc6DLqpbcqNVAwh).

You need one FRQ from chapters 1, 2 or 3, one FRQ from chapter 4 and one FRQ from chapters 5, 6 or 7.

See attached list for FRQs listed by chapter. All FRQs are available from CollegeBoard here:

http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html#free-response

This is assignment is due no later than 7:19am on Monday, January 4, 2016. It is expected that this

project will take between 4 and 6 hours. This assignment is worth 50 points.

Each FRQ can earn 15 points:

3 points: Creativity and originality, yet plausible.

4 points: Proper modeling after a published College Board question.

4 points: Neatness and clarity of question wording and question format.

4 points: Accurate and neat solution.

There are an additional 5 points for following all directions, submitting the type written questions via

Dropbox (https://www.dropbox.com/request/RGmEiYc6DLqpbcqNVAwh), overall neatness and effort.

All questions must be unique and your own work. Any questions found copied from a textbook, website

or other source, will results in an automatic zero (Z).

Mrs. Daniel will not be reading email after 2pm on December 18, 2015. Please plan accordingly.

2011 AP® STATISTICS FREE-RESPONSE QUESTIONS

© 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

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STATISTICS SECTION II

Part A Questions 1-5

Spend about 65 minutes on this part of the exam. Percent of Section II score—75

Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. A professional sports team evaluates potential players for a certain position based on two main characteristics,

speed and strength.

(a) Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating more desirable (faster) speeds. From previous speed data for all players in this position, the times to run 40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of 4.40 seconds, as shown in the table below.

Mean Standard Deviation Minimum

Time to run 40 yards 4.60 seconds 0.15 seconds 4.40 seconds

Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to

believe that the distribution of 40-yard running times is approximately normal? Explain.

(b) Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater)

strength. From previous strength data for all players in this position, the amount of weight lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below.

Mean Standard Deviation

Amount of weight lifted 310 pounds 25 pounds

Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.

(c) The characteristics of speed and strength are considered to be of equal importance to the team in selecting a

player for the position. Based on the information about the means and standard deviations of the speed and strength data for all players and the measurements listed in the table below for Players A and B, which player should the team select if the team can only select one of the two players? Justify your answer.

Player A Player B

Time to run 40 yards 4.42 seconds 4.57 seconds

Amount of weight lifted 370 pounds 375 pounds

Mrs. Daniel- AP Stats Sample “Create Your Own FRQ” Modeled after FRQ: 2011 #1 Emory University considers two major student achievement factors in its admissions process: unweighted high school GPA and SAT scores (Math and Critical Reading, only). Higher unweighted high school GPAs are considered more desirable by the admissions committee. All GPAs are calculated on a 4 point scale, where the maximum GPA is a 4.0. Based on previous admission’s data the mean GPA for admitted students is 3.63 and the standard deviation is 0.19.

Mean Standard Deviation Maximum

GPA 3.63 0.19 4.00

A. Based on the relationship between the mean, standard deviation, and maximum GPA, is it reasonable to believe that the distribution of unweighted high school GPAs approximately normal? Explain. B. Higher SAT scores are considered more desirable by the admissions committee. Based on previous accepted student’s data, the mean SAT score for admission is 1340 and the standard deviation is 40 points. Calculate and interpret the z-score for a student applying to Emory with a SAT score of 1490. C. Unweighted high school GPA and SAT scores are considered to be of equal importance to the admissions committee when selecting a student for admission. Based on the information about the means and standard deviations of the GPA and SAT scores for all players and the measurements listed in the table below for Students A and B, which student should be admitted if the committee can only select one of the two students? Justify your answer.

GPA SAT Score

Student A 3.86 1390

Student B 3.69 1400

FRQ Year #

Textbook Chapter Topics Name

2000 3 1 Graphing and comparing frequency distributions Flexibility ratings2001 1 1 Outliers Rain in LA2002 5 1 making graphs and comparing distributions Student/Faculty obstacle course times2004 1 1 Boxplots, outliers, properties of boxplots, shape/center Gasoline additives2005 1 1 Shape, center, spread of a distribution Test scores2006 1 1 Comparing distributions, variability, center Catapults2007 1 1 Stemplots, describing distributions Economics test scores2010 1 1 Comparing boxplots, constructing a stemplot, stemplot vs. boxplot Polluted rivers2011 1 1 Estimating median from hist., comparing hist., mean vs. median Pupil-teacher ratio2015 1 1 Comparing boxplots, making decisions using boxplots Accountant salaries2006 1 2 Cumulative frequency plots Monthly sales2008 1 2 comparing boxplots, rescaling data, mean/median and shape Sugar in cereal2009 1 2 Boxplots, median/IQR, linear transformation of data Gasoline Taxes2011 1 2 Assessing Normality; calculating, interpreting, and comparing z-scores Speed and strength1998 2 3 Histograms/scatterplots Number of defective items1998 4 3 Regression output, residuals Weed killer1999 1 3 Regression output, interpret slope+intercept, residuals Commercial aircraft2000 1 3 Describing scatterplots drug strengths2002 4 3 Regression output, correlation, infl. Points Commercial Airlines2002 1 3 scatterplot, interpret r, r2 swine/ammonia2003 1 3 influential points Work/Study relationship2005 3 3 residual plots, interpreting slope, r-sq, extrapolation railcars/fuel consumption2007 4 3 LSRL, residuals, influential points Father/Daughter heights2012 1 3 Describing scatterplots, influential points Sewing Machines2013 6 3 Comparing distributions, trends in timeplots, moving averages Typhoons2014 6 3 Calculate/interpret residuals, comparing associations, multiple regression Fuel consumption rate (FCR)2015 5 3 Describing scatterplots, classifying individuals, making a prediction Body shapes1999 3 4 Exp. vs. obs. study, confounding variables, cause-effect Dentist and apples2000 5 4 Exp. Design, blocking, double-blind Cholesterol drugs2001 4 4 Blocking, purpose of randomization Forest2002 2 4 Matched pairs experiment, double blind Waterproofing Boots2002 3 4 Design of Experiments, blocking Magnets and pain relief2003 4 4 Random assignment, control groups, generalizibility Yoga vs. Tai chi2004 2 4 Selection and response bias Dining Hall survey2004 2 4 Blocking, random assignment within blocks Shampoo2005 1 4 comparing stemplots, generalizibility, sampling variability Urban vs. Rural caloric intake2006 5 4 response, treatments, units, rand., replication, confounding Tractors2006 5 4 Treatments, randomization, limiting variability, generealizibility Tiger shrimp2007 2 4 Control groups, random assignment, blocking Dog joint and hip health2007 3 4 Block design, randomization Heat gain of windows2008 2 4 non-response bias School board survey

2009 3 4 Random Assignment, Non-random assignment Frog Dissection2010 2 4 Simple random sampling and stratified random sampling Cafeteria food survey2010 1 4 Treatments, units, response variable; scatterplots and linearity Garlic Oil2011 2 4 Exp. vs. obs. study, scope of inference, purpose of random assignment Fear of heights2011 3 4 Cluster sampling vs. stratified sampling New carpet in apartments2013 2 4 Convenience samples, selecting an SRS, stratified sampling Appearance of a university2014 4 4 Mean vs. median, sampling methods and bias Alumni income survey2001 3 5 Simulation using random digit table coupon simulation2003 2 5 Conditional probability, independence Age and Income relationship2009 2 5 Conditional Probability, Prob. Rules ELISA testing2011 2 5 Conditional probability, independence, segmented bar charts Politics and gender2014 2 5 General multiplication rule, informal inference, simulation design Selecting convention attendees1998 6 6 Normal dist, simulations, expected value Pearls, simulation1999 4 6 Normal, Binomial, Outliers Batteries1999 5 6 Sample space, Expected values Dice2001 2 6 Expected Value copy machines2002 3 6 Normal Dist, combining RV’s Relay Team2002 2 6 probability, expected value, conditional prob. airline overbooking2003 3 6 Normal, binomial neck sizes2004 3 6 Binomial, probability, interpreting probability, generalizibility brontosaurs2004 4 6 Probability rules, expected value antibiotics2005 2 6 Mean and SD of RV, combination of RV's Child and adult tickets2005 2 6 expected value/median relationship, sampling variability mean vs. median of discrete RV2006 3 6 Normal, binomial, inverse normal Golf balls2008 5 6 Combining normal RV's, normal calculations Snake Gulch Railway2008 3 6 Expected value, probability rules and distributions Josephine and Crystal Arcade game2010 3 6 Binomial distribution, binomial probabilities Multiple choice questions2010 4 6 Mean and SD of binomial, binomial probability, stratified sampling New car customer survey2011 3 6 Geometric prob, binomial prob, cumulative binomial Flight upgrades2012 2 6 Discrete probability distributions, expected value, normal calculations Spin the Pointer2013 3 6 Normal calculation, sum of random variables Eggs2015 3 6 Discrete probability distributions, expected value, conditional probability ATMs1998 1 7 Sampling distibution of sample mean Sampling distributions2004 3 7 Normal and sampling distribution of xbar Bauxite cars2006 3 7 Normal, binomial, sampling dist of xbar Depth measurements2007 3 7 Sampling dist of x-bar, normal dist, CLT Big Town Fisheries2007 2 7 probability distributions, binomial, sampling dist of xbar Number of pets2008 2 7 Properties of estimators: bias and variability Estimators2009 2 7 InvNormal, Binomial, Sampling Dist of x-bar Stopping Distances2010 2 7 Sampling distribution of the sample mean Rock-and-roll songs2012 6 7 Selecting a SRS, SE(mean) for SRS vs. stratified random sample Soft drinks2014 3 7 Normal probability, sampling dist of xbar, probability rules School attendance2015 6 7 Choosing a sampling method, comparing variability of sample means Tortillas