Monday, Monday, Monday....

AP EXAM FORMS/$ DUE TOMORROW! This will count as a grade for our class! You either turned your form in on time with EXACT CHANGE (100%), or you did not (0%). Get them in!

Tonight's homework: please complete the following in your textbook...CHECK OUT THE HINTS/TIPS BELOW!

Page 446: #3 (even though this is one problem, I expect to see lots of writing if you want full credit tomorrow!)

• For each scenario (a,b,c,d), define p, p-hat, the sample, the population, and check the 3 conditions (random sample, 10% condition, np and nq>10)
• Conditions = how we determine if we can use the methods of this chapter (a one proportion z-interval)
• The parameter of interest, p, is what we're trying to estimate--look at the question!
• So, for a, our p (what we're estimating) is "the percentage of all cars that may be unsafe"
• P-hat represents our sample percentage, or the percentage we actually collect data to calculate
• For these contexts, we do not know the value of "p." So, when we check our conditions, you will have to use p-hat for the success failure condition!
• In other words, your condition is: n(p-hat)>10 and n(1-phat)>10
• For example, in a, we first find p-hat = 14/134 = .1045...
• Condition: (134)(.1045) > 10 and (134)(1 - .1045) = (134)(.9955) > 10
• If we know a sample is not random, we can say:
• "It's not stated if this is a random sample, we will proceed with caution." OR
• For example, in context b, we KNOW we have a voluntary response sample (not random)--so it would not be correct to state that we can assume this is a random sample!
• The back of the book is very helpful for p, p-hat, sample and proportion...
• The information about "whether we can use the methods of this chapter" is also informative, but we would show our conditions differently (see below)

Here are the answers for the conditions (so you can check yours!--check p, p-hat, population, and sample in the back of the book):

a.) We can assume the police stopped a random sample of 134 cars; 134 cars is less than 10% of all cars; (134)(.1045) > 10 and (134)(.9955) > 10

b.) This is a voluntary response sample (not random), so we will proceed with caution; 602 is less than 10% of all viewers; (602)(.811) > 10 and (602)(.189) > 10

c.) This is a voluntary response sample (not random), so we will proceed with caution; 380 is NOT less than 10% of all parents/households (1245). We CAN NOT use a one-proportion z interval!

d.) We will assume our sample (all freshmen) is representative of all students at this school; 1632 may be less than 10% of all students at this school; (1632)(0.85) > 10 and (1632)(0.15) > 10

Take Home Quiz and Study; updated Saturday with an explanation of parameters v. statistics...

You have two responsibilities this weekend...

1.) Complete the chapter 18 take home quiz provided in class (or below). You MUST SHOW WORK for questions 2, 3, 7, 8, and 11 or you will not receive credit! I expect you to work hard and use your resources to figure this out! We will be starting new stuff on Monday, no exceptions! Step up to the challenge and make yourself (and me) proud!

2.) Study! We will start class on MONDAY with our CHAPTER 18 VOCAB QUIZ! (List below).

• We did not cover all of the terms in class! Use the definitions below! Even if you were out, you're taking this quiz--so study, study, study! No excuses!

Here are some hints/info about your take home quiz (by question)!

I also recommend the 4 videos the AP Stats Guy has! (Link on the right; they are videos 1-4 under Unit 5!)

1. Read carefully here! Use your notes about parameters and statistics, or maybe even check some definitions on page 287 of your textbook!
2. This question asks about the "mean number of admissions"--since it's about the "mean of a sample," we'll have to use a sampling distribution! Take a look at the key provided in class today for last night's homework for a sample problem, or look at the "step by step" example on pages 423-424 in your book! (if you don't have the key I provided today, you can also take a look at the 2010 AP Scoring rubric online, linked in yesterday's post below).
3. Here, we have a sampling distribution for proportions, b/c the question is asking us about a "% of a sample!" This is based on the ideas/math we discussed today in class....or, check out the "step by step" example on pages 415-416!
4. Think about what type of data we are collecting, then check your notes--we discussed when we use each type of sampling distribution depending on the type of data we collect!
5. See #4's hint.
6. You might look back at the table we created in our notes with the correct symbols for statistics/parameters from chapter 12! Or, you can find this table on p. 276 of your book!
7. Back to the sampling distribution for proportions...take a look at the table we created in our notes (Thursday) for the correct mean/standard deviation formulas! 
8. See #3's hint.
9. This deals with an idea called the "Law of Diminishing Returns" that we may or may not have discussed today in class. Either way, you can find more about this on page 423 of your book!
• It comes down to this concept: if we quadruple our sample size (n x 4) we only cut the standard deviation in half (divide by 2) because of the square root in the formula! 
• Also, remember, if we increase sample size we will decrease standard deviation...
• If we take a smaller sample, we will increase standard deviation...
10. See #9's hint.
11. See #2's hint.

Chapter 18 Vocab List and Definitions:

• Sampling Distribution (a plot of sample statistics taken from repeated samples)
• Sampling Variability (the expected differences we see in sample statistics)
• Standard Error (an estimated standard deviation based on sample statistics)
• Central Limit Theorem (the sampling distribution for means is approximately Normal, and is more approximately Normal as the sample size increases)
• 10% Condition (our sample must be less than 10% of the entire population)
• "Large Enough Sample" Condition (we need a large sample unless the population is Normal)
• Conditions for a Sampling Distribution for Proportions (10%, random sample, np and nq>10)
• Conditions for a Sampling Distribution for Means (10%, random sample, large enough sample)
• Sampling Distribution for Means is use with quantitative data
• Sampling distribution for proportions is used with categorical data
• As n increases, standard deviation of a sampling distribution decreases
• Remember, a sampling distribution question will ask about the mean of a sample or the % of a sample...

I got an email question about understanding population parameters vs. sample statistics--check out the explanation! Not only will this help you with this weekend's work, but it is the guiding principle behind next week's topic, confidence intervals.

Population Parameters vs. Sample Statistics:

A population parameter refers to any number that summarizes an entire population; a population parameter may be a mean, for example, the average age of all of the people in the world. Or, it may be a proportion--the percentage of all of Earth's water that is salt water. A parameter could be a standard deviation, a third quartile (Q3), a minimum, a range--anything, as long as it summarizes the population. For instance, the minimum GPA of all students in CT high schools might be a parameter, as it summarizes the population, "all high school students in CT." Although we may not know the value of a parameter, there is some true value; for example, there is an actual, set/fixed age of all humans, or an actual minimum GPA of all hs students in CT, we just don't know what it is

In most cases, we do not know the values of population parameters; it would be nearly impossible to calculate the values above--imagine trying to find the average age of all humans--by the time you found everyone, millions of people would have been born and passed. Some parameters, we do know, like the % of Earth's water that is salt water. Most of the time, we don't know the values of population parameters; one of the most valuable uses for Statistics is to try to estimate these parameters. We try to use sample statistics to estimate parameters; maybe we're trying to estimate the % of all CT residents who will vote for Bernie Sanders, or the median income of all households in Hartford county, or the average amount of rainfall in Florida each year. Even though we don't know these values, they do exist, and they are some fixed value.

Generally, it's too time consuming, cost effective, and sometimes impossible to survey/study an entire population, so we use sample statistics to try to estimate these population parameters. Samples are much more realistic options, and we can use them to accurately predict the values of population parameters.

Sample statistics are values that summarizes samples--any mean, median, standard deviation, IQR, maximum, etc. is a statistic if it is summarizing a sample of data. When we survey 400 students from CT high schools and ask their GPA, then find the mean, minimum, standard deviation, etc. these are statistics because they summarize a sample. We also know that if we take many samples, they will not all yield the same statistics; if you and I both took samples of 400 CT students, we would not get the same sample mean or minimum etc. This is sampling variability (or sampling error)--the idea that sample statistics will vary for different samples, However, in our coming chapters, we will see that we can develop an understanding of how much they vary, and can use this to predict the values of parameters.

So, sample statistics are different for different samples. But by understanding how these sample statistics will vary, we can use them to accurately predict the fixed value that is the population parameter.

Take Home Quiz Questions:

Thursday HW

Period A--I changed my mind...tomorrow's class will start with a stamp problem where you check conditions rather than a pop quiz.

Tonight, please complete the 2 AP problems provided in class (or below). Here are some hints:

• For part a of the 2010 FR, when asked to "describe the sampling distribution," you must....
• First, check conditions (like #23 from last night's hw)
• Then, define the shape, center, and standard deviation of the sampling distribution
• For question b of the 2010 FR, you need to calculate a probability using the sampling distribution--take a look at today's notes about rainfall in Ithaca, NY!
• Remember, a sampling distribution is about the mean of a sample...
• So, if we have 160 minutes for 4 songs, to exceed the time limit the average length of a song would have to be longer than 4 minutes! (160 min/40 songs = 4 min per song, on ave)
• Check out the AP Scoring Rubric! (2010)
• On the back, you can approach this problem in two ways..
• You can skip the conditions for the problem on the back about the elevator, b/c this was a multiple choice question on the AP exam (skip conditions for MC!).
• First, you could use a sampling distribution for means--think about what the mean of the sample (of 3 men) would have to be over if their total weight exceeds 700 lbs! (In other words, what would the average weight for one male exceed if the 3 men combined are over 700 lbs?)
• Then, use the sampling distribution/Normal model math like our Ithaca example!
• OR....\
• You could approach this problem as we did in chapter 17...
• You could use the individual weights to find the mean and standard deviation if we combine three weights (remember, we can't add standard deviations...Pythagorean Theorem of Statistics...)
• Then, we can use this new mean and standard deviation (and the Normal model) to find the probability that the total weight exceeds 700 lbs!

Tomorrow we will wrap up our notes on Sampling Distributions. You will have a multiple choice take home quiz for homework, and our chapter 18 vocab quiz will be on Monday! Here's the list:

• Sampling Distribution (a plot of sample statistics taken from repeated samples)
• Sampling Variability (the expected differences we see in sample statistics)
• Standard Error (an estimated standard deviation based on sample statistics)
• Central Limit Theorem (the sampling distribution for means is approximately Normal, and is more approximately Normal as the sample size increases)
• 10% Condition (our sample must be less than 10% of the entire population)
• "Large Enough Sample" Condition (we need a large sample unless the population is Normal)
• Conditions for a Sampling Distribution for Proportions (10%, random sample, np and nq>10)
• Conditions for a Sampling Distribution for Means (10%, random sample, large enough sample)
• Sampling Distribution for Means is use with quantitative data
• Sampling distribution for proportions is used with categorical data
• As n increases, standard deviation of a sampling distribution decreases
• Remember, a sampling distribution question will ask about the mean of a sample or the % of a sample...

Wednesday HW

Ok, now we can finally get back to a normal routine and a bunch of 5 day weeks...sorry I was out!

Tonight, verify that the conditions are met for the following contexts in your book:

Page 428-429: 7b, 11, 23

• For each, check the 3 correct conditions (you'll have to decide which sampling distribution to use...)
• Then, if the conditions are met, write a sentence stating, "A sampling distribution for ______ is appropriate."

Tomorrow (in class) we'll start to look at the next step of the process (after the conditions)--the math! We'll ultimately be using this to start to build an understanding of confidence intervals! (Starting Monday!)

Remember, your AP forms/$ are due this Tuesday, March 1st! Don't forget!

Weekend...

This weekend, please complete the "Exploring Sampling Distributions" worksheet provided in class. We discussed much of this in class over the past two days...however, you need to use your textbook and your brain to figure out the following...

• For #2, you need to define the shape, mean, and standard deviation for a sampling distribution for proportions--check the box at the bottom of page 414, and record this information (using appropriate notation).
• Similarly, for #4 you need to define the shape, mean, and standard deviation for a sampling distribution for means--check the box on page 421.
• On the back, you are asked to hypothesize about the shape of three different sampling distributions...
• For example, for #5, you are asked to consider the shape for a sampling distribution for maxima; so, imagine that we take a sample, find the max, and plot it. Then we repeat. As we continue to do this, where do we expect most of the maxima to be? (left? middle? right?) What shape does this result in?

Here are the links to the applets we explored in class--if you were out, we used these to develop our notes in class on Thursday/Friday!

Sampling Distribution for Proportions Applet (Reese's)

Sampling Distribution for Means Applet

• With this applet you can create sampling distributions other than means, including the median! You can use this to help you with #6.

We'll finish our notes on sampling distributions and do some math problems (with them) on Monday and Tuesday! See you there!

Thursday HW!

Don't forget that your AP money is due on March 2nd!

Tonight, please complete the 6 (review) multiple choice questions provided in class!

I'm checking! I need to see some work written on your paper to receive full credit! You will earn a 0 if you only have 6 answers circled!

Tomorrow in class we'll get deeper into sampling distributions, with the goal of finishing up on Monday! Be ready to learn lots of stuff!

Hope you aced your vocab test today!  See you in the am!

If you were out (or lost yours), here are the 6 multiple choice questions:

Unit 3 (Methods of Data Collection) Vocab Test Tomorrow!

Tomorrow we will start class with our Unit 3 vocab test! 

There are 35 words, each worth 2 points. STUDY!

Here's the vocab list for tomorrow in case you were absent:

After the vocab quiz we'll get back to discussing Sampling Distributions! We'll wrap that up on Friday/Monday, and then it's on to confidence intervals! Woooooohoooooo!

TAKE HOME TEST DUE WEDS. 2/17!

Happy February Break!

Over break, be sure to complete your "Unit 3: Methods of Data Collection" take home test! This test is worth more points than any you've taken this year--you are expected to take your time, use your notes, and use your textbooks (chapters 11, 12, 13) to complete this test! I will be tough in grading it, because you have a lot of time and a variety of resources to use! If, for some reason, this is late, you will lose 10 points for each day it's late.

Remember, for chapter 13, experiments, you will have to teach yourself much of the content--use your textbook, use some of the links on the right, watch some videos--be responsible! Be "AP"! Step up and rise to the challenge!

The take home test is uploaded under our "Resources: Powerpoints, Assignments..." link on the right, in case you need (another) copy.

Here are the links to the answer keys/scoring rubrics for the blocking problems we did in class yesterday:

2004 Scoring Rubric (Shampoo)

2001 Scoring Rubric (Forest)


Also, remember that when you return we will have our Unit 3 Vocab Test (chapters 11, 12, 13) on Thursday, 2/18. Start studying now!

Good luck on your take home test! And enjoy your break! Rest up, relax, and come back recharged for some hard work--this is our last big stretch before the AP exam, and we're going to learn lots of interesting, awesome, and very important stuff! See you there!

When we return we will start some "new stuff," with chapter 18: sampling distributions! The math we start to do when we return is based on the Normal model--so, if you review your chapter 6 notes you'll be better prepared when we return! We'll be doing lots of z-scores and normalcdf( stuff again!

For example, this will be our stamp problem when we come back--if you want to get ahead, do some review and do this over break! (= extra stamp if done). It's all based on chapter 6 (zscores, Normal model):

Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY gets an average of 35.4 inches or rain each year, with a standard deviation of 4.2 inches. Rainfall amounts can be described by a Normal model.

a.)   During what % of years does Ithaca get more than 40 inches of rain?

b.)   During what proportion (%) of years does Ithaca get between 30 and 40 inches of rain?

c.)    What amount of rainfall marks the 90th percentile? (Or, in other words, what amount of rainfall cuts off the top 10% of rainfall amounts)?

Weds. HW = Take Home Quiz!

Tonight, please complete the 19 multiple choice questions provided in class (all are based on ch. 13, experiments and observational studies). Use your textbook to help with these questions!

1. Complete the 19 multiple choice questions. 
2. Record your answers on separate paper. I will collect this tomorrow. You must number each question and provide the correct answer--if these questions are not numbered, your quiz will not be scored! If you do not have these answers recorded on separate paper BEFORE you come into class your paper will not be accepted.

THIS WILL ONLY BE ACCEPTED TOMORROW! BE SURE TO HAVE IT DONE OR YOU WILL EARN A 0 ON A QUIZ!

If you were absent (or lost your packet) you are still expected to do this! You can find the questions under our "Resources: Powerpoints, Assignments..." link on the right! 

Tomorrow in class we will discuss confounding variables a couple other details about experiments...then, it's on to February break! See you there!

Tuesday HW: Teach Yourself Experiments!

Tonight, be sure to complete the "ch. 13 reading questions" below. Tomorrow you will start class with a short (10 minute) quiz based on experiments--you will be able to use these answers on your quiz!

Remember that YOU ARE RESPONSIBLE TO TEACH YOURSELF CHAPTER 13! We will still have our take home test over break, which includes content about experiments. Also, we will have our unit vocabulary test (ch. 11, 12, 13) the Thursday after break!

Oh, and one more thing...tomorrow you will have 19 multiple choice questions for homework, which will be collected and graded (on Thursday). If you'd like to get a head start (b/c you already did your reading questions), you can find these questions under our "Resources: Powerpoint, Assignments, and More..." link! You can write your letter answers on a separate piece of paper for me to collect! (I want you to keep the packet/questions to use over break). 

Chapter 13 Challenge: Teaching Yourself Experiments and Observational Studies

Part I: Read the chapter and complete each of the questions below. Remember, this is for your benefit; the more thorough your notes/responses are, the better prepared we will be! 

·        These questions serve as an outline to help guide your reading. Of course you can take additional notes to strengthen your understanding!

1.      There are two types of observational studies—retrospective and prospective studies.

a.      What is a retrospective observational study?

b.      What is a prospective observational study?

c.      What is matching in an observational study? (page 305).

2.      In an experiment where does the random assignment occur?

3.      What is/are the factor(s), levels, and treatment(s) in an experiment?

4.      What is the response variable?

5.      What distinguishes an experiment from the other methods of data collection? In other words, how is an experiment different than a simulation, sample survey, and observational study?

6.      Describe/comment on each of the four principles of experimental design:

a.      Control:

b.     Randomize:

c.      Replicate:

d.     Block:

7.      What sampling method is equivalent to blocking in an experiment?

8.      *Read through the step-by-step examples in the chapter; these are the examples we would have discussed for our notes in class!

9.      Explain the meaning of “statistically significant.”

10.   What is a control treatment/control group?

11.   What does it mean for an experiment to be single-blind or double-blind?

12.   What is a placebo? Why do we use placebos?

13.   What does it mean for two variables to be confounded?

14.   In your own words summarize the procedure for the tomato/fertilizer experiment on page 298 -300.

**Note the vocabulary list on page 310-312. This list shows the words that you are responsible to know for our chapter 13 vocab!

Important Snow Day Update! Read This!

First off, enjoy your snow day! I'm about to head out for a little snow adventure with my dog and I'm pumped!

After you have some fun outside, it might be a good idea to have a productive day (and Saturday) so you can enjoy Super Bowl Sunday and have a ton of homework Monday night...because we lost today's class, we will have to finish chapter 13 (experiments and observational studies) in 3.5 days! This means you will have an extended set of "reading questions" for homework Monday night. You will be responsible for teaching yourself much of the vocabulary by reading your textbook (and using any other resources you like). You may have an open-note quiz to start class on Tuesday (based on these reading questions). We will use our 3.5ish (minus quiz time) days in class to address any questions you have, and to review some of the "trickier" concepts with experimental design. Experimental design will absolutely be on your Feb. break take home exam, and we will have our (methods of data collection) unit vocabulary test the Thursday after we return from break.

Anyway, back to the more immediate future....

You have two homework responsibilities this weekend (one due Monday, one Tuesday):

1.) Complete your two bias AP problems, then use the rubrics in the post below to score each. Remember, this homework counts double. (See yesterday's blog post for more on this assignment).

2.) Complete the "ch. 13 reading questions" below for Tuesday. I'd strongly recommend getting a head start--get at least half of it done, so you don't have to do it all Monday! You may have an open-note quiz to start class on Tuesday (based on these reading questions). Remember, you are trying to teach yourself this content. Your responses to these questions serve as your primary notes for the chapter (I would answer them in your notebook with the rest of your notes!). The more effort/time you put into reading/responding to the questions, the better you'll understand experimental design for your test and the AP exam! So don't just look for the answers to these questions, read the whole chapter! Oh, and if you have these reading questions entirely done for Monday, you'll get a few points added to (your score on) that free response problem we completed in groups. And 3 stamps (extra credit!)

Chapter 13 Challenge: Teaching Yourself Experiments and Observational Studies

Part I: Read the chapter and complete each of the questions below. Remember, this is for your benefit; the more thorough your notes/responses are, the better prepared we will be! 

·        These questions serve as an outline to help guide your reading. Of course you can take additional notes to strengthen your understanding!

1.      There are two types of observational studies—retrospective and prospective studies.

a.      What is a retrospective observational study?

b.      What is a prospective observational study?

c.      What is matching in an observational study? (page 305).

2.      In an experiment where does the random assignment occur?

3.      What is/are the factor(s), levels, and treatment(s) in an experiment?

4.      What is the response variable?

5.      What distinguishes an experiment from the other methods of data collection? In other words, how is an experiment different than a simulation, sample survey, and observational study?

6.      Describe/comment on each of the four principles of experimental design:

a.      Control:

b.     Randomize:

c.      Replicate:

d.     Block:

7.      What sampling method is equivalent to blocking in an experiment?

8.      *Read through the step-by-step examples in the chapter; these are the examples we would have discussed for our notes in class!

9.      Explain the meaning of “statistically significant.”

10.   What is a control treatment/control group?

11.   What does it mean for an experiment to be single-blind or double-blind?

12.   What is a placebo? Why do we use placebos?

13.   What does it mean for two variables to be confounded?

14.   In your own words summarize the procedure for the tomato/fertilizer experiment on page 298 -300.

**Note the vocabulary list on page 310-312. This list shows the words that you are responsible to know for our chapter 13 vocab!

Thursday HW: Bias

ANY/ALL MAKEUP WORK REGARDING SIMULATIONS/SAMPLES/EXPERIMENTS MUST BE DONE 3:15 PM, WEDNESDAY, 2/10!

Tonight, please COMPLETE AND SCORE the two AP Free Response questions provided in class. The questions are below (if you lost yours or were out), and the rubrics are also below (so you can score your response). 

This homework will count double: half of the credit for DOING each problem, half for SCORING each.

Ch. 12 Vocab Quiz Tomorrow!

Tonight, please complete the 2011 Free Response question (provided in class, or below).

Tomorrow we will start class with our chapter 12 vocab quiz! Study! Here's the list:

• Simple Random Sample
• Stratified Sample
• Cluster Sample
• Systematic Sample
• Multistage Sample
• Convenience Sample 
• Voluntary Response Sample
• Census
• Response Bias
• Nonresponse Bias
• Voluntary Response Bias
• Undercoverage
• Bias
• Sample
• Sampling Frame
• Population
• Population Parameter (of Interest)
• Sample Statistic
• Sampling Variability/Sampling Error
• Response Variable

2011 Free Response (Homework):

And lastly, here is the 2011 AP Scoring Rubric (Answer Key!)

Want to see one more example of how sampling might show up on our AP Exam? Try the 2014 Free Response on the back of your homework! If you do this BY FRIDAY you can earn homework extra credit!

2014 AP Scoring Rubric

Tuesday HW and Articles to Read!

Tonight, please complete the following in your textbook (regarding bias):

Page 289-291: 17, 19, 21, 31 (Period A: Notice this is changed--31 replaces 5!)

Tomorrow (in class) we'll start with some multiple choice (in our groups), then we'll look at some examples of how to write about bias, and we'll finish up with another AP problem! See you there!

If you have some time, here are two interesting things I recently read online...

• Niche.Com: Top Colleges (Rankings) 

• Read This! Especially if you're thinking about a major in Statistics! It's about the role of Stats (in college)... 

Monday HW!

Tonight, please complete the "Chapter 12: Sample Surveys!" worksheet provided in class! 

Tomorrow (in class) we'll finish our notes on bias; then, on Wednesday we'll do some practice, and on Thursday we'll have our chapter 12 vocab quiz! At least that's the plan...

Enjoy your Monday! Do your homework!