Chapter 10 2020 Teacher Notes with Guided Explanations and AP Exam Thoughts

Hi once again all (beautifulllll peeeeople😊)!

I have attached the 10 page 2020 Chapter 10 teacher notes to a recent email since we did NOT officially get to these in class.  We are not yet entirely sure how much of this material is “fair game” for the 2020 AP Exam.  However I give it to you here as a start for now with an added bonus: Teacher thoughts for focus and further clarification for each page to read as you go through them:

Chapter 10 2020 In Class Teacher Notes Important “Take Aways”/Explanations:

Page 1:

• Look at the two Calculator Functions at the top of the page that we will use in 10.1 (2 proportions) as a preview for getting most things that we need for the DO Step in Confidence Intervals and Null Hypothesis Significance Tests this section 😊.
• Whenever we describe a distribution in AP Stats in Semester 1 (Chapters 1-6) we use SOCS; but, in 2020 Semester 2 (Chapters 7-10) we only need to do Shape Center Spread.
• Read the description and formula for comparing 2 proportions ( p-hat_{1  minus}  p-hat₂ ) on the first half of this page 1.
• Ex a) “two bags of colored beads” on the second half of page 1 displays how you would go about describing a distribution for  2 proportions ( p-hat_{1  minus}  p-hat₂ ).  Notice how similar this is to Section 7.2 Sampling Distributions of p-hat “Reese’s Pieces” in your in class Chapter 7.2 notes.  It just involves a little more work because you are now taking the difference between two proportions.  BE CAREFUL:  Notice that in the Spread formula you always add under the radical.  This comes from a concept learned in Semester 1, but the good news is it’s on the formula sheet😊!

Page 2:

• Ex b) See how finding a requested probability for 2 proportions ( p-hat_{1  minus}  p-hat₂ ) is very similar to what we did in Semester 1 except this time you use the difference values for your data (given as -0.02) and parameter (see part a : - 0.1) values for the numerator and the SD (see part a : 0.0971) for the denominator of the z-score needed.
• Ex c)  This is a nice review of the “less than 5% condition” for being surprised or not plausible.
• On the second half of the notes for this page 2 titled 10.1 Notes- Confidence Intervals for p_{1 –}  p_2: Read about the formula breakdown for the confidence interval and notice how it is similar to the formula for a 1 proportion confidence interval (1-Prop z-Int) Chapter 8-2.  The inference method that you should state (which is the calculator function that you will use 😊) for this 10.1section however is 2 Prop z-Int (because there are 2 proportions that you are taking a difference of).

Page 3:

• The top half of the page simply review the conditions from section 8.2 (with a little more work because there are 2 proportion instead of 1) that need to be met for this section 10.1 (and stated in the Plan step) for a confidence interval: Random, Normal, Independent.
• Example 1 “President Obama’s rating change from 2009 to 2010” takes us through the four step process (State Plan Do Conclude) for the construction of a 90% 2 proportion confidence interval for the given set of data.
• This page gives the work for State and Plan

Page 4:

• The first ¾ of this page gives the work for the Do and Conclude steps for the four step process for Example 1 “President Obama’s rating change from 2009 to 2010”.
• This year (2020 AP Stats Exam) If you simply copy exactly what your calculator gives in the 2-Prop ZInt windows you should feel confident in getting full credit for the Do step 😊.
• MAKE SURE THAT YOUR INFERENCE METHOD  2-Prop ZInt APPEARS SOMEWHERE IN YOUR FOUR STEP PROCESS.
• Notice that the Conclude statement  is similar to that for a 1 proportion confidence interval (1-Prop z-Int) Chapter 8-2.
• Part b) reminds us about how a value appearing in an constructed confidence interval (in this case the value is “0”) gives plausibility or SUPPORT FOR THE NULL HYPOTHESIS (a statement of no difference – which can mean the difference is zero).

Page 5:

• Read this this page titled 10.1 Day 3 – Significance Test for p_{1 –}  p₂ simply get a feel for the foundation for the  four step process for a Null Hypothesis Significance Test for p_{1 –}  p₂.
• Note the Inference Method 2 prop z Test in the very last statement at the bottom of the page 😊.  

Page 6:

• This page gives the work for the four step process (SPDC) for Ex1 “The National Sleep Foundation”.
• This year (2020 AP Stats Exam) If you simply copy exactly what your calculator gives in the 2-Prop ZTest windows you should feel confident in getting full credit for the Do step 😊.
• MAKE SURE THAT YOUR INFERENCE METHOD  2-Prop ZTest APPEARS SOMEWHERE IN YOUR FOUR STEP PROCESS.
• Notice that the Conclude statement  is similar to that for a 1 proportion significance test (1-Prop ZTest) Chapter 9.2.

Page 7:

• This page gives the work for the four step process (SPDC) for Ex2 “GM study to help employees stop smoking”.
• Notice that amount of work that I show for each step here is MORE THAN SUFFICIENCE for full credit for a question of this kind 😊.
• This year (2020 AP Stats Exam) If you simply copy exactly what your calculator gives in the 2-Prop ZTest windows you should feel confident in getting full credit for the Do step 😊.

Page 8:

• Look at the two Calculator Functions at the top of the page that we will use in 10.2 (2 means) as a preview for getting most things that we need for the DO Step in Confidence Intervals and Null Hypothesis Significance Tests this section 😊.
• Whenever we describe a distribution in AP Stats in Semester 1 (Chapters 1-6) we use SOCS; but, in 2020 Semester 2 (Chapters 7-10) we only need to do Shape Center Spread.
• Read the description and formula for comparing 2 means ( x-bar_{1  minus}  x-bar₂ ) on the first half of this page 1.
• Example 1 a) “potato chip manufacturer” on the second half of page 1 displays how you would go about describing a distribution for  2 means ( x-bar_{1  minus}  x-bar₂ ).  Notice how similar this is to Section 7.3 Sampling Distributions of x-bar in your in class Chapter 7.3 notes.  It just involves a little more work because you are now taking the difference between two means.  BE CAREFUL:  Notice that in the Spread formula you always add under the radical.  This comes from a concept learned in Semester 1, but the good news is it’s on the formula sheet😊!

Page 9:

• Ex b) See how finding a requested probability for 2 means ( x-bar_{1  minus}  x-bar₂ ) is very similar to what we did in Semester 1 except this time you use the difference values for your data (given as -0) and parameter (see part a : 5) values for the numerator and the SD (see part a : 8.732) for the denominator of the z-score needed.
• The follow-up question is a nice review of the “less than 5% condition” for being surprised or not plausible.
• On the second half of the notes for this page 9 ,read about the formula breakdown for the confidence interval and notice how it is similar to the formula for a 1 mean confidence interval (Z-Interval when sigma is known vs. T-Interval when sigma is unknown) Chapter 8.3.  The inference method that you should state (which is the calculator function that you will use 😊) for this 10.2 section however is 2 Samp ZInt when sigma is known OR 2 Samp TInt when sigma is known  (because there are 2 means that you are taking a difference of).  As with Section 8.3, the population sigma is RARE:Y KNOWN, so you can count on using the T-DISTRIBUTION: 2 Samp Tint for your Inference Method and Do step. “Samp” stands for Sample.
• You WILL NOT use the Degrees of Freedom formula at the bottom of the page.  You will just copy the answer from your calculator in the Do step 😊.  Yes df is (strangely) decimal most times in this section, don’t worry abut that, just copy it down from the calculator!

Page 10:

• The top 3/4 of this page: Example 2 a) gives the work for State Plan Do and Conclude steps for the four step process for “Target versus Mejier bags” for a 99% 2 difference of means confidence interval confidence interval for the given set of data.

• This year (2020 AP Stats Exam) If you simply copy exactly what your calculator gives in the 2-Samp TInt windows you should feel confident in getting full credit for the Do step 😊. Always select NO for the Pooled section (“No” should be the default).
• MAKE SURE THAT YOUR INFERENCE METHOD  2-Samp TInt APPEARS SOMEWHERE IN YOUR FOUR STEP PROCESS.
• Notice that the Conclude statement  is similar to that for a 1 mean confidence interval (T-Interval) Chapter 8.3.
• Part b) reminds us about how a value appearing in an constructed confidence interval (in this case the value is “0”) gives plausibility or SUPPORT FOR THE NULL HYPOTHESIS (a statement of no difference – which can mean the difference is zero).

Page 11:

• Read this this page titled 10.2 Day 2 Hyp Tests – 2 sample t/z test Mu_{1 –}  Mu₂ simply get a feel for the foundation for the  four step process for a Null Hypothesis Significance Test for Mu_{1 –}  Mu₂.
• Note the importance of knowing the difference between “paired” versus “unpaired” data  at the bottom of the page 😊.  

Page 12:

• This page gives the work for the four step process (SPDC) for “Bounty versus generic paper towels”.
• Notice that amount of work that I show for each step here is MORE THAN SUFFICIENCE for full credit for a question of this kind 😊.
• This year (2020 AP Stats Exam) If you simply copy exactly what your calculator gives in the 2-Samp TTest windows you should feel confident in getting full credit for the Do step 😊.
• MAKE SURE THAT YOUR INFERENCE METHOD  2-Samp TTest APPEARS SOMEWHERE IN YOUR FOUR STEP PROCESS.

I have also attached to this email a word doc copy of this as well as the 2020 AP Stats formula sheet for your reference in case you misplaced it (though I’m told it is also on the College Board website).

P.S.  I plan on watching a webinar AP 2020 Exam Updates with Trevor Packer this evening.  I’ll let you what I find out after processing what is revealed.

******NOTE:  I HIGHLY RECOMMEND THAT YOU WATCH THE COLLEGE BOARD LESSONS HERE  https://apstudents.collegeboard.org/coronavirus-updates/ap-course-schedule (Go to: 2-2:45 Statistics)

  ALTHOUGH THE CB EXAM SELECTED INSTRUCTORS ARE GIVING US THINGS NOT DIRECTLY ON THE EXAM THIS WEEK, BUT STARTING NEXT WEEK THEY WILL BE INSTRUCTING US ALL (TEACHERS & STUDENTS) ON THE CONTENT, STRATEGIES FOR SUCCESS, AND THE FORMAT OF THE 2020 AP STATS EXAM.  WE WILL PRACTICE AND LEARN TOGETHER 😊😊😊

As always, please email me with any questions, comments, thoughts.

Take Care!!