The Wknd

This weekend, please complete the following in your textbook:

Page 290: 11, 13, 15, 27 (Use the sampling method definitions below in case we did not get to them all in class!)

**Simple Random Sample, SRS: when we randomly select individuals from a group so that each person/thing is equally likely to be chosen, and each sample (group) is equally likely; this is like pulling names out of a hat, or assigning each person/thing a number and then generating random numbers (ignoring repeats) to collect your sample
**Stratified Random Sample: when we split people into groups (strata) based on some characteristic related to the response variable, then we randomly sample some people/things from each group/strata
**Cluster Sample: when we split people into groups (clusters) (each cluster is ideally representative of the population), then we randomly select one (or more) clusters, then survey everyone/thing in that cluster
**Systematic Sample: when we survey every "nth" person; for instance, we might take a list of all students, start at a random number, then survey every "15th" person on the list
**Convenience Sample: when we survey those people/things that are easy (convenient) for us; no randomization
**Voluntary Response Sample: when we give people the option to respond to a survey, such as an online poll, or if I mail out a survey for people to return; no randomization
**Multistage Sample: this is when we combine multiple methods from above; however, remember that SRS is an inherent part of a cluster or stratified sample--so creating strata then randomly sampling from each group is a stratified sample, not multistage


Enjoy! On Monday in class we'll finish our notes on sampling strategies and start to discuss bias! See you there!

Oh, and I'm definitely checking your homework!

Have a great weekend!

TAKE HOME QUIZ!

Tonight, please complete the "Pop Quiz: Sample Surveys" provided in class (or below). This will be collected and graded as a take home quiz!

• We will not have a quiz to start class tomorrow....this is the quiz you would have taken...you have it as a take home to save us some class time...

Here are the answers to last night's homework so you can check and use these to help with your take home quiz!

Here is the take home quiz in case you lost yours or were out:

Pop Quiz: Sample Surveys

1.       Employees of Fenway Park plans to survey people who have been to the park and ask, “How would you rate your experience at Fenway Park (using a scale of 1-10 as a quantitative measure)?” During one baseball game, the employees randomly select 1,000 seat numbers and survey these 1,000 people at the park.

Identify each of the following. (each @ 2 points)

a.)    Sample:

b.)    Sampling Frame:

c.)     Population:

d.)    Population Parameter of Interest:

e.)    Sampling Method:

2.       For each scenario below identify the population parameter of interest. Within your answer define the context in detail, and clearly identify what the population is. (each @ 2 points)

a.       A meteorologist plans to take a random sample of 30 towns in CT and record the amount of rainfall over the past year.

b.      An psychologist takes a random sample of 5,000 students from colleges/universities across the country and asks, “Do you remember the dream you had last night?” 

Wednesday HW

Tonight, please complete the worksheet where you are "Analyzing Contexts" provided in class (many of you grabbed this yesterday).

Remember, we have a quiz on Friday to start class--the quiz is just like this homework! If you can ace tonight's homework, you'll be ready for the quiz!

Here are the questions in case you lost yours or were out:

For each statistical study below identify the following:

a.       The population

b.      The population parameter of interest

c.       The sampling frame

d.      The sample

e.      The sampling method, including if randomization was employed

f.        Any potential sources of bias or problems in generalizing to the population

1.       A question posted on the Lycos Web site on 18 June 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes.

2.       Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city’s election districts. Staff members go there and interview all the residents they can find.

3.       Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm re-inspected until purity is restored.

Tuesday...

No official homework tonight! Enjoy your night off!

Or, feel free to get a head start! Here's tomorrow night's homework:

For each statistical study below identify the following:

a.       The population

b.      The population parameter of interest

c.       The sampling frame

d.      The sample

e.      The sampling method, including if randomization was employed

f.        Any potential sources of bias or problems in generalizing to the population

1.       A question posted on the Lycos Web site on 18 June 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes.

2.       Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city’s election districts. Staff members go there and interview all the residents they can find.

3.       Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm re-inspected until purity is restored.

Tomorrow we'll get back into our chapter 12 notes! See you there!

Monday HW/Quiz Tomorrow!

Tonight, please complete the 2014 Free Response question provided in class (or below)! (A little forced studying!)

The first two parts (a and b) are a little probability review! Then, part c brings in the "simulation" aspect!

After you finish the free response, be sure to check your answers with this link: 2014 AP Scoring Guidelines/Rubric!

Tomorrow we will start class with our simulations quiz! Here's what's on it:

• 1 simulation: write a procedure, simulation (using a given random number table), then write a conclusion!
• 1 short answer: explain why a simulation fails to model reality correctly (like our stamp...)
• 2 simulation multiple choice questions!
• You will have roughly 20 minutes to complete the quiz! Be ready!

If you want to study some more (for tomorrow's simulation quiz), try the two problems on your slides that we never did in class! (There is one about McDonald's Monopoly and one about a multiple choice quiz!)

Here are the procedures (so you can check/study!)

McDonald's:

1.) Generate 2 digit numbers from 00-99 (or 1 digit #'s from 0-9).

2.) Let 00-09 represent St. Charles' Place, 10-69 represent States Avenue, and 70-99 represent Virginia Avenue. (Or, let 0 represent St. Charles, 01-06 represent States, and 7-9 represent VA).

3.) Generate random numbers until you have one of each of the three Monopoly pieces. (*Note: we do not have to ignore repeats, because we can repeatedly get the same piece)

4.) Record the number of items we had to purchase to obtain all 3 pieces. 

5.) Repeat; conduct 10 trials.

Conclusion: Based on the simulation, we expect a person to purchase ______ items, on average, to obtain all 3 Monopoly pieces.

Multiple Choice

1.) Generate 2 digit numbers from 00-99. (Or, 1 digit numbers from 0-9).

2.) Let 00-19 represent a correct response, and 20-99 represent an incorrect response. (Or, 0-1 represent correct, 2-9 represent incorrect). (*Note: since you are "guessing blindly" you have a 1 in 5 chance to guess correctly, or a 20% chance to be correct--that's why we use these number breakdowns).

3.) Generate 5 random numbers (representing the 5 quiz questions). 

4.) Determine and record if all 5 questions were correct (yes or no).

5.) Repeat; conduct 10 trials.

Conclusion: Based on the simulation, the probability that she answered all 5 questions correctly by blindly guessing is _____. (To find this probability, take the number of times she got all 5 correct divided by your 10 trials.)

Friday HW/Vocab Quiz Monday!

This weekend you have two responsibilities:

1.) Please complete the AP Free Response problem provided in class (or below)! Add part c!

• I accidentally cut off part c! After you design a simulation (procedure) and then simulate, I need you to interpret your results:
• Part c: "Based on your simulation, how many prizes do you expect to award each week?

Here's a link to the AP scoring rubric (2001) so you can check your homework answer! Scroll down to question 3.

2.) CHAPTER 11 VOCAB QUIZ TO START CLASS ON MONDAY! Here's the list:

• Random (Outcome) (in your notes or ch. 11 glossary)
• Pseudorandom Number (in your notes or ch. 11 glossary)
• Component (in your notes or ch. 11 glossary)
• Outcome (in your notes or ch. 11 glossary)
• Trial (in your notes or ch. 11 glossary)
• Response Variable (in your notes or ch. 11 glossary)
• Simulation (in your notes or ch. 11 glossary)
• Experiment (in your notes)
• Sample Survey (in your notes)
• Observational Study (in your notes)
• Then, there are three more questions--you are given a context and asked to identify the:
• Component (remember, this is the "most basic outcome." Think--when we look at a random number, what are we using it to represent happening? For our in class examples, the component was "having a child," or "picking a student for the dorm."
• Outcome: think about what you might label each number as--for our in class examples, we had two outcomes--either "girl or boy" for our first example, or "varsity or not varsity" for our dorm example
• Response Variable: remember, this is what you are measuring; for our in class examples, the response variable was "number of children in the family," or "whether or not all 3 students selected were on the varsity team"

And here is the procedure for the back of the paper we did today: You are about to take the road test for your driver's license. You hear that only 34% of candidates pass the test for the first time. This percentage rises to 72% on subsequent retests. Estimate the percentage of those tested who still do not have a driver's license after two attempts.

1. Generate two digit random numbers from 00 to 99.
2. For the first test, let 00-33 represent passing and 34-99 represent failing.
3. For any tests after the first test, let 00-71 represent passing and 72-99 failing.
4. Generate a random number; if the student passes, the trial is ended. If the student fails, generate one more (a second) random number. (Do not generate more than 2 numbers).
5. Record whether or not the student passes within two tries.
6. Repeat.
7. Find the % of times that a person did not have their license within two attempts.

Thursday HW = Important Practice!

Tonight, please complete the following in your textbook:

Page 266-268: 13, 19, 23

• For each; 1.) Write a procedure 2.) Simulate using a random number table 3.) Interpret your results (answer the question!)
• Conduct 5 trials for each simulation (not 20).
• I'm checking!
• Here are some hw hints:
• For each problem, consider: do you have to ignore repeats? Can a student repeatedly get multiple choice questions correct? Can a student repeatedly fail a driving test? If we draw a customer's coupon to win a prize, would we (repeat) and draw that customer's number again?
• #13: Think: how many random numbers should you generate to represent the test? Also, consider what numbers should represent a question being "right" or "wrong."
• #19: This is a tough one. This will be a simulation with "extra steps," because the probability of passing the driving test changes! In this example, someone has a 34% chance of passing on their first attempt, but they then have a 72% chance of passing any test after that! You also have to keep in mind that if a student passes the first time they will not take the test again, they're done. But, if a student fails the first time, they have to continue to take the test with a 72% chance to pass.
• #23: For this problem, you will have multiple (more than 2) categories represented by random numbers, as there are 4 different prizes that may be given out. When should you generate random numbers until? (When will the store stop handing out coupons)?

Remember, each simulation is different; our notes attempt to outline a generic process for writing a procedure, but each individual context will be a little different--you have to THINK about each situation! It's essential you get practice!

Tomorrow we'll do some classwork; then, on Monday we'll have our chapter 11 vocab quiz. Then, we'll start our notes on chapter 12. 

On Tuesday we'll start class with a chapter 11 quiz (a simulation).Then, we'll continue our chapter 12 notes. 

Oh...does anyone want a free copy of NBA 2K15? I just got 2K16 so I don't need it anymore! It's for XBox One. If you want it, email me and I'll raffle it off amongst all the emails I get! carofano.fm@easthartford.org.

Wednesday HW

Tonight, please write a procedure for the following contexts in your book:

Page 266: 9, 25

• Again, for each situation, simply write a procedure for a simulation just as we did in class.
• A full procedure would answer questions a,b,c for #9
• For 25, we can only write the procedure; tomorrow we will learn how to actually simulate and interpret our results

Also, don't forget your AP exam paperwork! (Due March 2nd)

• Get it in sooner rather than later so you don't have to worry about it!

Tomorrow we'll discuss how to actually simulate trials, and then we'll look at the conclusion. After that, it's just a matter of trying different problems and different contexts--practice makes perfect! See you all there!

Oh...and here are the homework answers--this might be more helpful (or less confusing) than the back of the book!

9.) You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. But you're worried that only 100 students will show up to vote. How often will the underdog (the one with 45%) win? Set up a simulation.
1.) Generate two digit numbers from 00-99.
2.) Let 00-54 represent votes for the favorite (your candidate)
Let 55-99 represent votes for the underdog.
3.) Generate 100 random numbers; record who each voter (random number) votes for (F or U).
4.) Next, count the number of votes for each (favorite or underdog) and determine the winner of the election.
5.) Repeat. Conduct many trials.
6.) Find how often (out of the total # of trials) the underdog will win (or the probability the underdog wins).

25.) Many couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each gender, what would the average family size be? Assume that boys and girls are equally likely.
1.) Generate one digit numbers from 0 - 9. (OR, generate 2 digit numbers from 00-99).
2.) Let 0-4 represent boys, and 5-9 represent girls (OR, let 00-49 represent boys, and 50-99 represent girls).
3.) Generate random numbers until a family has both a boy and a girl.
4.) Record the family size.
5.) Repeat; conduct many (20) trials.
6.) Find the average family size after 20 trials. 

Tuesday HW = First HW of Q3 = Counts Double!

Tonight, please complete the chapter 11 reading questions provided in class (or below).

• Since this is our first homework of the third quarter, it counts double! Start off on the right foot!

See you tomorrow for some more notes/discussion of simulations! Happy Tuesday!

Midterms and Tuesday's HW

Midterm scores are in! There was an error in the initial scoring of the exams; all scores have been corrected and are in the grade book. Your score may have changed from last night, so check again! 

Tuesday night's homework is at the bottom of this post; do it this weekend! It might be a bigger homework for just Tuesday night!

Check out these awesome articles relating to the powerball and probability! With all the insanity surrounding powerball there have been tons of awesome probability-related articles all over social media...these are two of my favorites!

• Things Less Likely Than Winning Powerball
• Can You Guarantee A Powerball Jackpot?

Back to the midterm...here's how I arrived at your grades. First, I graded each person's exam and found the raw score--that is, I found the % of multiple choice you answered correctly and the % (of 20) possible free response points you earned. I then found the average of these two scores to get your overall "raw score." This data is shown below...

Next, I had to convert the raw scores to a projected/predicted AP exam score. For instance, on the AP exam, if you answer 50% of the exam correctly, you will definitely earn a 3. Each year these "cut score" fluctuate, depending on the difficulty of the exam. I used past cut scores, as well as the distribution of scores on last year's exam, to arrive at these cut scores for our test:

Next, I took all of the raw scores and listed them in order. I used the cut scores to establish who would have an A/5, a B/4, etc. Then, within each letter grade (A,B,C..) I converted the raw score to a midterm exam score. So, if you earned a B on the exam, that's projected to be a 4 on an AP exam...if you scored a D, that's a projected 2, and so on... (You can use this list to go backwards from your exam score (online) to see what your actual raw score was). 

Ultimately, we did ok. Some of us did well, others could have done better. I took away these things from this exam:

1. Many of us underachieved. I believe this is due to a lack of preparation (studying). For instance, many A students in period D earned C's (3's) on the midterm. Or, in period E, too many students earned 1's and 2's. This underachievement is 100% based on preparation. To succeed on the AP exam it's all about how you study.
2. We're in a good spot. Although I feel many of us could have done better, we're in a pretty good spot. We did ok on this.
3. There is still a lot of work to be done. Just because you earned an A on the midterm, that does not guarantee you a 5 on the AP exam--we still have a lot to learn, and the test in May will have more/different questions. Similarly, if you earned a D (2), that doesn't mean you will do so in May. Maybe you'll really like and be really good at the new stuff we learn, and you will improve your score in May.
4. We have the potential to have the highest % of students passing the AP Stat exam in the history of EHHS. This can occur IF we continue to work hard and IF we put a significant amount of time and effort into preparing for the AP exam (outside of class).

(And when I say "we," that includes me as well. I also have to work hard, to prepare more outside of class, and to continue to grow and learn to help us all dominate this AP exam in May.)

Here's the overall data for the projected AP scores, both by class and overall:

New unit on Tuesday! Be ready...it's a new quarter, a fresh start, new seats...come with a positive attitude and be ready to work! Enjoy your long weekend!

If you don't want to have any homework Tuesday night, do it this weekend! Your homework is to use your textbook to answer each of the following:

MIDTERM!

STUDY! Of course the midterm is going to be a challenging test, and a stressful two hours...but it's also an excellent opportunity for us to see where we stand in our preparation for the AP exam! The midterm is essentially a mini practice exam, so it will give us valuable information to predict how you might do on the AP exam in May! Take it seriously, prepare yourself, and give your best effort next week!

It is absolutely essential that you STUDY. If you do not prepare yourself, you can likely expect a D or an F on the midterm! 

• There is an outline of all topics on the midterm exam under our classroom resources link.

• There is also a guide of "ways to study" under our classroom resources link!

• Or, check out this article: Here Are 6 Scientifically Proven Tips for Studying!

• Another idea to study is by using the review exercises in your textbook...these come at the end of each unit and provide miscellaneous practice problems for each unit; we covered unit (the textbook calls them parts) 1, 2, and 4. These reviews start on pages 130, 244, and 402. If you do the odd problems, you can find the answers in the back of the book

• Finally, another great way to study (maybe the best way?) is to try various released free response questions (from past AP exam). You can find ALL of these, along with the scoring rubrics, with this link: All Released AP Free Response and Scoring Guidelines (Answers)!

Also, remember that STAMPS ARE DUE ON THE DAY OF YOUR EXAM (or earlier)! 

• Same deal...count your stamps (double check), and write the total on the front
• Fasten your stamps together (somehow) with your name and the total on the front!
• If your total is incorrect, you will get a 0--so count twice!

See you all next week! Be ready to get an A! STUDY, STUDY, STUDY!


Oh, and one more thing...here are the answers to the practice multiple choice and open ended classwork problems we did today in class!

Back to Real Life!

It was great to get back and see you all today!

Check out this awesome article about the powerball--lots of probability! Can You Guarantee A Powerball Win?

No official homework...just STUDY! 

First and foremost, use the answer keys provided in class today (or below) to check your sub work! This is the first way you should begin to prepare for the AP exam--if you didn't finish the sub work (review packets), finish! Then, use the keys provided to check your work! If you aren't checking, you aren't using your time productively! (There's no value to practicing if you don't make sure you're practicing correctly)!

Also, remember that STAMPS ARE DUE ON THE DAY OF YOUR EXAM (or earlier)! If I were you, I would count them up and turn them in tomorrow so you don't have to worry about them next week!

• Same deal...count your stamps (double check), and write the total on the front
• Fasten your stamps together (somehow) with your name and the total on the front!
• If your total is incorrect, you will get a 0--so count twice!

Lastly, remember there is an outline of the midterm exam topics along with a list of different ways to study under our classroom resources link! Use them!

See you all tomorrow!

• **There is a mistake in the answer key below; for multiple choice question #4, the answer is B (my explanation on the right says the answer is "extrapolation," but I accidentally put the wrong MC letter**