Monday HW!

Monday HW: Tonight please complete the "packet" provided in class (or below). 

• An answer key for tonight's hw is also posted below. 

    

Today's Class Recap:

• Stamp = finding our sample statistic and ME given only the interval
• HW Q's: #8 and 38a discussed in class, also addressed any other HW q's
• Be sure to check the conditions for any "full interval" question (like 13
• Ch. 19 Notes: 
• What is a point estimate
• How can we find ME and a point estimate given only a confidence interval? ("top right slide")
• What is the meaning of the confidence level?---how can we interpret a given confidence level?

• Tuesday: ch. 19 practice (AP FR and MC)
• Wednesday: goal = ch.19 quiz on this day, then intro to ch. 20 (hypothesis testing)
• Thursday and Friday: ch. 20 notes (one proportion z tests)

Monday HW Answer Key:

• 1 (Finding sample size; A state's dep't of education....): n = 179 applications
• 2 (find point estimate and ME given a CI; A sales company....): 
• a.) 90.5% = 0.905 = p-hat
• b.) 4.5% = 0.045 = ME
• 1 (How often do Americans dine out?)
• a.) p-hat = 0.18 = 18%
• b.) ME = 0.04 = 4%
• 2 (A poll of 2,017 likely voters...) 
• C Level = 95% (z* = 1.96)
• 3 (A survey found that 69%...)
• ME = 2.38%
• 4 (A study was recently conducted...)
• Interval = 67.5% to 72.5%

Self-Assess Your Understanding of Confidence Intervals!

• It is absolutely essential that you make sure you're on top of all this interval stuff--not only do we have a quiz on Wednesday, but we also know that these concepts will be repeated multiple times over the remainder of AP Stat!

• What do I need to know about confidence intervals?
• When/why do we create a confidence interval?
• What symbol is a sample proportion/%? A population proportion %? (statistic v. parameter)
• How do we identify/calculate x, n, and p-hat for a given context? 
• What wording in a question suggests I have to create a CI?
• How do I find the critical value for a given C. Level using...
• t-table 
• invnorm(
• What is the full CI process?
• How do I check conditions for a one prop z interval?
• How do I do the math with my calculator and show the supporting formula? 
• How do we interpret the meaning of a confidence interval?
• How can we use our confidence intervals to assess some claim? (like 13d from the weekend hw)
• What is ME? 
• How can we calculate margin of error given a sample size, C. Level, and p-hat? 
• How can we calculate sample size for a given ME?
• How does changing n affect the ME? the width of an interval?
• How does changing C. Level (and as a result, z*) affect the ME? the width of an interval?
• How can we find the value of p-hat (a point estimate) only given an interval? 
• How can we find the ME only given an interval? 
• What does it mean to say "__% confident?"--how can we interpret the meaning of a confidence level? 

• If you have any questions, things you're confused about, or just want a deeper understanding, take the time this weekend to use your resources!
• Watch AP Stat Guy videos 6-9 in Unit 5 for some help!
• Click Me! AP Stat Guy Videos!
• Use Khan Academy--this is aligned with AP Stat!
• Linked on the right WITH a course code
• Google stuff--anything about one proportion z intervals!
• Do this now! If you try to assess your own learning this weekend, then you have Monday/Tuesday to come see me for any help before our quiz--don't wait until it's too late?

Fri-yay!

Responsibility #1: Weekend HW 

• Pages 446-448: 7, 8, 13abd, 27a, 31ac, 35, 38a
• For 7,8: when it says, "for a given" or "for a fixed" or "for a specified" it means that values is staying the same...
• So "for a given sample size," means, if n stays the same, "reducing ME will mean lower confidence"--T or F? (that's #8 a)
• For 13a DON'T FORGET CONDITIONS!
• For 27a consider the sample size(s)...
• For 31ac....use today's notes/example from class!
• What do you notice--how much larger of a sample did we need to cut the margin of error in half (from 6% to 3%)?
• How could you have answered (c) without using the "finding n" formula?
• For 35, more finding n--use today's notes/examples!
• For 38a, "explain why the poll is actually inconclusive" means "explain why we cannot conclude that the amendment will win" (based on this poll and confidence interval) 

Responsibility #2 = Self-Assess Your Understanding of Confidence Intervals?

• It is absolutely essential that you make sure you're on top of all this interval stuff--not only do we have a quiz on Wednesday, but we also know that these concepts will be repeated multiple times over the remainder of AP Stat!

• What do I need to know about confidence intervals?
• When/why do we create a confidence interval?
• What symbol is a sample proportion/%? A population proportion %? (statistic v. parameter)
• How do we identify/calculate x, n, and p-hat for a given context? 
• What wording in a question suggests I have to create a CI?
• How do I find the critical value for a given C. Level using...
• t-table 
• invnorm(
• What is the full CI process?
• How do I check conditions for a one prop z interval?
• How do I do the math with my calculator and show the supporting formula? 
• How do we interpret the meaning of a confidence interval?
• How can we use our confidence intervals to assess some claim? (like 13d from the weekend hw)
• What is ME? 
• How can we calculate margin of error given a sample size, C. Level, and p-hat? 
• How can we calculate sample size for a given ME?
• How does changing n affect the ME? the width of an interval?
• How does changing C. Level (and as a result, z*) affect the ME? the width of an interval?
• How can we find the value of p-hat (a point estimate) only given an interval? (Monday's class)
• How can we find the ME only given an interval? (Monday's class)
• What does it mean to say "__% confident?"--how can we interpret the meaning of a confidence level? (Monday's class)

• If you have any questions, things you're confused about, or just want a deeper understanding, take the time this weekend to use your resources!
• Watch AP Stat Guy videos 6-9 in Unit 5 for some help!
• Click Me! AP Stat Guy Videos!
• Use Khan Academy--this is aligned with AP Stat!
• Linked on the right WITH a course code
• Google stuff--anything about one proportion z intervals!
• Do this now! If you try to assess your own learning this weekend, then you have Monday/Tuesday to come see me for any help before our quiz--don't wait until it's too late?

Responsibility #3: Catch up on HW!

• I will accept any/all chapter 19 (confidence interval) HW for full credit on Monday
• You'll have to come show me before school/after school/during study hall if I don't have time to check in class....
• Check PowerSchool to see if you're missing anything or have only partial credit (all grades are up to date)
• AFTER MONDAY I WILL NOT ACCEPT ANY MORE LATE HW!

Today's Class Recap:

• Stamp = finding n multiple choice
• HW Q's: #37 and #11
• Be sure to check the conditions for any "full interval" question (like last night's slide)
• Ch. 19 Notes: 
• How can we use a given ME to find sample size? (bottom right slide)
• Solving an equation!
• How does changing sample size and confidence level affect...
• Margin of error?
• the width of an interval?
• (Created a table in our notes to summarize this info)

Next Week's Plan:

• Monday: finish ch. 19 notes
• Stamp = T/F (like 7, 8 from hw)
• What is a point estimate?
• How can we find the value of a point estimate and the margin of error only given an interval?
• What does the confidence level actually mean?
• Tuesday: finish any ch. 19 notes (if necessary), ch. 19 practice (FR?)
• Wednesday: goal = ch. 19 quiz on this day, then intro to ch. 20 (hypothesis testing)
• Thursday and Friday: ch. 20 notes (one proportion z tests)

Thursday HW

Tonight you have two responsibilities for HW:

1.) Complete the "bottom left slide" provided in class today (or below)--this was posted yesterday, so you may have it done already! If so, nice job!

• FULL interval process (conditions, math = calculator screen and formula, interpret interval)

2.) Please also complete the following in your textbook:

Pages 446-448: 11, 37

• For 11b don't stress too much, try to explain what ME means and then use the answer in the back of the book to help you understand this idea
• The concept in 11e will be one of the main concepts we address in class tomorrow--you got this!
• For 37--more math! All math here! Set up a formula using the given margin of error, solve for z*, and then use this to determine the confidence level!
• C. Level = normalcdf(-z*, +z*, 0, 1)

Weekend HW (if you want to get a head start)!

• Pages 446-448: 7, 8, 13abd, 27a, 31ac, 33, 37, 38a
• For 31ac....
• What do you notice--how much larger of a sample did we need to cut the margin of error in half (from 6% to 3%)?
• How could you have answered (c) without using the "finding n" formula?
• For 38a, "explain why the poll is actually inconclusive" means "explain why we cannot conclude that the amendment will win" (based on this poll and confidence interval)

Today's Class Recap (stupid delay shortening class):

• Stamp = pop classwork assignment! (if you were out today you will do this tomorrow)
• Ch. 19 Notes: the CI formula and the AP formula sheet
• Margin of Error
• How do we calculate margin of error (ME)? (middle left slide)
• What is margin of error? (definition)
• How can we use a given sample statistic and ME to create a confidence interval?
• Intro to Finding N
• How can we use a given ME to find sample size? (bottom right slide)

"Bottom Left Slide" (tonight's HW) Answer Key:

• Conditions:
• We will assume this is a random sample of 2,002 25-32 year old Americans.
• 2,002 is less than 10 % of all 25-32 year old Americans
• (2002)(0.53) > 10   and   (2002)(0.47) > 10
• A one proportion z-interval is appropriate.

• Math:
• One Prop Z Int:
• (0.50124, 0.5587) = 0.53 +/- 2.576 sqrt(0.53 x 0.47 / 2002)
• p-hat = 0.53
• n = 2,002
• x = (0.53)(2002) =1061

• Interpret:
• We are 99% confident that the true percentage of all employed 25-32 year old Americans with a bachelor's degree who are "very satisfied" with their current job falls between 50.124% and 55.87% based on this sample of 2002 25-32 year olds. 

Tonight please complete the "AP Stat Stamp" worksheet (but it's not really a stamp) about the % of females in the labor force (provided in class or below). 

• Be sure to complete the full process! Conditions, math, interpret your interval
• Use 95% confidence (so we all get the same answers)
• Write everything/show all work as you would on the AP exam to earn (full) hw credit!

If you feel like getting ahead, at some point we will have the problem below for homework--go ahead and complete this on separate paper if you like!

• If for some reason we did not have this as homework I will count it as extra credit...

Today's Class Recap:

• Stamp = creating a confidence interval! (math and interpret)
• Went over stamp
• How do we show the "math" work on the AP exam (with the CI formula)?
• Ch. 19 Notes: the CI formula and critical values
• What is a critical value (z*)?
• How do we find the value of z* for a given confidence level using....
• invnorm
• T-table (provided in class)
• How is a confidence interval calculated? (breaking down the formula)
• Connect to formula sheet
• What is margin of error?

4 Day WkNd!

First and foremost, enjoy your loooong weekend! Take some time to relax, definitely do something fun, spend some time with friends/family, and also enjoy some time to yourself! Recharge those batteries because when we come back we have a looooong stretch of 5 day weeks up to April break, and this is the most critical time in AP Stat (for our exam preparation)!

This weekend you have a few responsibilities:

1.) Please complete the take home quiz provided in class (or below).

• Be sure to show ALL work for any question with a ** or you won't earn credit!
• For multiple choice #'s 5 and 7 you have to choose the correct formula for the one proportion z interval--this is based on today's work to develop that formula!
• For #7 you might need some help finding the "z*" or "critical value..."
• Extra Stamp Opportunity:
• Google "critical value" or "z*" and either do some reading or watch some video(s) about what this value is and how it is calculated/found
• Take notes! 
• You can earn up to 4 extra stamps depending on the level of detail in your notes--I'll collect these on Weds. (only Weds)
• Use your notes!

2.) If you did not do either hw from chapter 19 I will accept either/both for full credit on Wednesday!

• Both assignments are in the textbook--look at the blog posts from Weds. and Thurs. for the problems/directions

3.) Want to get ahead? Learn more about one proportion z intervals?

• Go to the AP Stat Guy videos (linked below or on the right)
• Look at Unit 5, Video #'s 6, 7, 8, or 9
• All of these videos deal with confidence intervals for proportions--some of them recap what we've learned, some will give you some insight into what's coming next!
• AP Stat Guy Videos! Click me!

Today's Class Recap:

• Stamp = x, n, and p-hat and conditions review (questions 1 and 2 from the "Investigating Confidence Intervals" activity)
• Worked in groups to develop the formula for a one-proportion z interval by completing the "Investigating Confidence Intervals" assignment
• If you were out this is below--do it so you're caught up!
• Use the example I passed out Monday of the 68/95/99.7 rule to help with #3
• #3 is the key to completing the rest--we're trying to figure out how an interval is calculated!

What's happening when we come back?

• When we return we'll spend some time breaking down the formula (that we developed today) more, with the following objectives for learning:
• Understanding the formula, why it looks the way it does, and how we can apply this same idea to means
• What is a critical value? How can we calculate (or look up) our critical values?
• How do we complete a "full" AP free response with confidence intervals? (practice)
• How can we calculate margin of error?
• How can we find sample size if we are given a margin of error?
• How can we find our point estimate and margin of error if we are only given an interval?
• What is a point estimate?
• How does changing sample size and/or our confidence level affect the margin of error? the width of an interval?
• Let's practice all that?

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

Thursday HW!

To all Juniors:

• Tomorrow we will work (in groups) in class to develop the formula for a one-proportion z interval. Please stop by to grab this assignment/investigation if you have not done so.
• You should complete this assignment over your long weekend
• Watch videos about the formula for a one proportion z interval if you need some more help/explanation!
• You will be responsible for knowing/understanding this stuff--the more effort you put into the classwork you missed, the better prepared you will be!
• Please get a copy of the notes from a classmate as well!
• Over the long weekend we have an assignment that I may collect and grade as a take home quiz. Please stop by tomorrow morning for a copy if you do not have one already.

• Another option: Juniors, if you would like, please feel free to attend period H (AP Stat) tomorrow. You are scheduled to have lunch at 11:35 to 2:10, which is H period. Of course if you're hungry and tired after a long day then EAT! Don't feel obligated, but this is an option for you. 

Thursday HW: 

• Pages 446-448: 5, 9, 21ab, 23bc
• For 5 your job is to determine which of the interpretations is correct, if any, and provide a bullet explaining why (like today's slide)
• For #9 interpret the given confidence interval!
• For 21a use your calculator to find the interval and copy your calculator screen as your math work, then interpret your interval for part b
• Please also write down the values of x, n, and p-hat
• For 23bc, same--part b = math = calculator screen, c = interpret
• Please also write down the values of x, n, and p-hat
• *Remember to always round n to the nearest whole number or you'll get an error on your calculator!

Today's Class Recap:

• Stamp = x, n, and p-hat
• Ch. 19 Notes
• What is the process for any confidence interval question?
• Conditions: what are they?
• Discussed a "tweak" for the success/failure condition
• Math: what do we show? 
• Also added notes on n, x, and p-hat
• Interpret 
• How do we interpret a confidence interval? 
• Provided a template for interpreting intervals in our notes
• Interpreted an interval and identified x, n, p-hat in our notes for a given context (3 slides given yesterday)
• Then, discussed which interpretation (also in those 3 slides) a-e was correct and what issues there were with the incorrect interpretations
• Learned how to create a one proportion z interval using our graphing calculator (tomorrow we'll investigate this formula)

Wednesday HW!

**If you were absent today you must make up your chapter 18 vocab quiz before the weekend! And be sure to bring your take home quiz in tomorrow!**

Tonight please complete the following in your textbook--use the instructions below (some are changed from the book)!

• Here's some stuff you need for tonight's homework before you start: 
• n = sample size (will be given in the question/context)           
• x = # of "successes" in a sample
• x = (n)(p-hat)              
• p-hat = % of "successes" in our sample
• p-hat = x/n
• Sometimes our question/context gives us p-hat and n, sometimes it gives us x and n; we have to know how to find each of these three values (x, n, and p-hat) in either scenario (both situations come up in this hw)

• Pages 446-449: (answers are posted below)
• 15 (For this question please simply provide the values of x, n, and p-hat.)
• Hint: x and n are given, you have to find p-hat....
• 21 (For this context provide the values of x, n, and p-hat AND check if the conditions for a one proportion z-interval are met)
• Hint: this time, p-hat and n are given, and you have to find x!
• Remember, when checking the conditions, we must use p-hat for our "success/failure" condition because we don't know the value of p
• 23a (For this question/context please verify that the conditions for a one proportion z-interval are met)
• Hint: in this context the values of x and n are given, you have to calculate p-hat

• Stamp for Tomorrow: (look up) and record the definition of statistical inference in your notes

Today's Class Recap:

• Chapter 18 Vocab (and conditions) Quiz = 13 min
• Ch. 19 Intro Notes
• Why do we use a confidence interval?
• What is a one-proportion z-interval?
• What is the process for any confidence interval question?
• Conditions: what are they?
• Discussed a "tweak" for the success/failure condition
• Math: what do we show? (Thurs)
• Also added notes on n, x, and p-hat
• Interpret (Thurs)
• How do we interpret a confidence interval? 
• Provided a template for interpreting intervals in our notes

HW Answer Key (for tonight's hw):

• 15.) n = 122, x = 78, p-hat = 78/122 = 63.934%
• 21.) 
• n = 2700, p-hat = 0.20 (or 20%), x = (0.20)(2700) =540
• This is a random sample of children (randomly selected from all parts of England)
• 2700 is most likely less than 10% of all children in England
• (2700)(0.20) > 10 and (2700)(0.80) > 10
• A one proportion z interval is appropriate.
• 23a.)  A one proportion z interval is appropriate because:
• This is a "random survey of 226 college students."
• 226 is less than 10% of all college students
•  (226)(0.0885) > 10 and (226)(1 - 0.0885) >10
• Note that you can also check this condition without using p-hat...
• The number of "successes" is 20, which is greater than 10, and the number of "failures" would be 226 - 20 = 206 which is also greater than 10
• Remember, this condition requires us to check that the number of "success" and the number of "failures" are both greater than 10, and in this case, the number of "successes" (or x) is directly given!
• Or check using p-hat as shown above!
• p-hat = 20/226 = 0.0885 (or 8.85%)