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Friday, February 23, 2018

Weekend HW!

You have two responsibilities for this weekend:

1.) Study for your chapter 18 and 19 vocab quiz! (start of class Monday)
2.) Complete the True/False worksheet (provided in class or below)
3.) Do the extra credit homework (provided in class or below)

  • You must correct any false statements (or re-write them to make them true)
  • You must create your own example to get full credit!
  • Please read below for help with statements d and f:
    • Read the "diminishing returns" section on page 423
    • And/or...consider this....
      • We know that as we increase sample size, we will decrease standard error and margin of error...
      • However, we also know that the "n" is under the radical (square root) in the formula for standard deviation/standard error...
      • Therefore, if we increase the sample size by taking a sample that is 4 times larger, it will only decrease the standard error/margin of error by cutting it in half. This is because of that square root--we took a sample that is 4 times larger, but we need to take the square root of 4 (2), so we cut the standard error/ME in half (divide by 2).
      • Or, if we take a sample that is 16 times larger we will make the standard error/ME smaller, but it will not be divided by 16--the standard error/ME will be "one fourth as large," or divided by 4 (because we need to take the square root of 16)
  • Here is the chapter 18/19 vocab list:
    • Use your chapter 18 vocab quiz (you did it with the sub and we went over the answers) to study!
    • Sampling Distribution
      • Be able to recognize a sampling distribution question
        • Remember, a question requires us to use the sampling distribution formulas for standard deviation (from our formula sheet) if the question asks for a percent/probability regarding the mean of a sample or the percent of a sample...
        • And you must be given sample size...
    • Sampling Variability
    • Standard Error
    • Confidence Interval
    • Critical Value
    • Margin of Error
    • Point Estimate (a single value used to estimate the value of a population parameter; this is our sample statistic, found at the center of an interval)
    • 10% Condition (sample size must be less than 10% of the population size)
    • WHY do we check the randomization condition? (to check that our sample is representative of the population)
    • WHY do we check (n)(p-hat)>10 and (n)(q-hat)>10? (to check that our sample is large enough)
    • Know how changing sample size and changing confidence level affect the margin of error and the width of an interval (Friday's notes!)
    • What does the "One" in "One Proportion Z Interval" refer to?
On Monday we'll finish up chapter 19 by going over our homework and discussing the meaning of our confidence level! Then, on Tuesday we'll do some classwork/practice, and on Wednesday take another quiz! See you there!

Here is the true/false homework:


And here is the extra credit homework:


Finally, if you're feeling super ambitious, here is Monday night's homework--we'll learn how to interpret confidence levels on Monday, but you can do the other stuff:

Page 446: 7, 14, 23d, 33


Thursday, February 22, 2018

Thursday HW

Hey everyone! I hope you all had a productive day today, and you feel confident finding a point estimate and margin of error given a confidence interval--there's a multiple choice question based on this idea on our chapter 19 quiz next week!

And don't forget to get your homework done if you didn't last night:

Page 447: 11, 31, 35, 37 

Tomorrow in class we'll explore and discuss how changes to our confidence level and our sample size affect both the margin of error and the width of an interval. Then, we'll get the definition of point estimate and margin of error in our notes, and quickly review what you learned today. If we have time, we'll discuss what a confidence level actually means, and examine how to answer the question, "Interpret the confidence LEVEL." If we can't get to this tomorrow, we'll cover it Monday after our chapter 19 vocab quiz. 

Then we'll look to have a (20 minute) chapter 19 quiz  to start class on Tuesday or Wednesday before we begin to learn about our next big concept for the semester, hypothesis testing!

I'm looking forward to getting back and working with you all tomorrow! See you there--hope you had an awesome and productive day!

Wednesday, February 21, 2018

Wednesday HW

Hey everyone! It's looking like Lincoln isn't getting any better, so there is a pretty good chance I'll be absent tomorrow--I apologize for having to miss class again, but I am 100% confident that you will all use this time productively to work together and to help one another learn some more chapter 19 stuff!

Because I'm not sure if I'll be here tomorrow I'm going to modify the homework--this will still be checked on Friday:

Homework:
  • Page 447: 11, 31, 35, 37 
  • This will be checked Friday, but I would do these tonight because they'll help you practice for tomorrow's classwork if I'm absent

Here's the plan for tomorrow depending if I'm here or not....
  • If I'm here tomorrow (Thursday)...
    • We will continue to work through chapter 19 and discuss....
      • Point Estimates
      • Finding ME and Point Estimate given an interval (bonus from the take home quiz)
      • Explore how changing sample size and confidence level affect the width of our interval
  • If I'm absent tomorrow (sub plans)....
    • This is an actual screenshot of the plans I've left for the sub:

I hope I get to see you all tomorrow--if not, be productive and ace your classwork! And work together to learn how to find the point estimate (p-hat) and margin of error given a confidence interval!

Friday, February 16, 2018

4 Day Weekend = Take Home Quiz!

This weekend please be sure to complete the "Confidence Intervals for Proportions Intro Quiz!" 

  • If you need a copy email me at carofano.fm@easthartford.org
  • Use your notes to ace this thing!
    • You can also check out the AP Stats Guy Videos--Unit 5 Videos #6, 7, 8, 9 if you need some help or missed some class time!
    • This take home quiz is a great summary of what you need to know about chapter 19 thus far!
Juniors/people who were out Friday: here's what you missed:
  • We DID NOT get to the stamp problem I gave you (juniors)--so don't worry about doing that! (That will be our stamp on Wednesday)
  • We start class by looking over a key for last night's homework--use this example/key (posted below) to check your homework and as an example!
  • In class we completed and scored the 2017 AP Free Response! Please get this done to best prepare yourself for success!
    • Here is the homework key:

    • Here is the 2017 FR question:
    • And here is the link to the 2017 Scoring Rubric so you can check your work and score your FR:




      When we return next week we'll finish up chapter 19 (Weds-Fri), and then we'll start the following week with some quizzes (vocab and math quiz).

      Here are some of the topics we're going to explore next week--feel free to read ahead in chapter 19 or do some independent research to get a head start!

      Chapter 19: Topics for Next Week...

      • Understanding margin of error...
        • What is margin of error?
        • How does changing sample size (increasing or decreasing n) affect ME?
          • How does changing n affect the width of an interval?
        • How does changing our confidence level (increasing or decreasing C. level) change ME?
          • How do changes in our C. level affect the width of the interval?
      • What is a point estimate?
      • How can we find the value of a point estimate (sample statistic) given only the interval?
      • How can we find margin of error given only an interval?
      • What does __% confidence mean? 
        • Interpret confidence LEVEL--we know how to interpret the interval, now we have to discuss how to interpret the level
      • How can we find sample size for a given margin of error?
      • How can we use an interval to "test a claim?"
        • We've done this! This was like #13d from our homework, deciding if our interval supported/contradicted a politician's claim that 1 in 5 auto accidents involved a teenage driver
      Feeling ambitious? Here is a textbook homework assignment for when we return:
      • I'm not sure when I'll assign these, or if I'll split them into multiple assignments, but at some point when we return we'll have to complete these textbook problems:
        • Page 447: 7, 11, 21c, 23, 29ab, 31, 35, 37 






      Thursday, February 15, 2018

      Thursday HW

      Tonight please complete the problem below (also found in our chapter 19 slides)

      • Question posted below--this is found on the second page of our slides--the top right and middle left slides are being used (or posted below)
      • Your task: "Estimate the percentage of all employed 25-32 year old Americans with a bachelor's degree who are "very satisfied" with their current job.
        1. First, check that the conditions are met.
        2. Next, "do the math," as we saw today in class...
          1. Use your calculator to get the interval and copy your calculator screen
          2. Show the interval formula (with #'s substituted)
          3. Use 99% confidence!
        3. Finally, interpret your interval!
      Tomorrow in class we'll practice some more with a 2017 AP Free Response problem! Next week we'll get more in depth with all this interval stuff, and we'll have a take home quiz over the long weekend!

      Juniors--good luck on the practice SAT! Stop by in the morning if you didn't get the assignments you'll miss (or your take home quiz) in class today!

      Have an awesome Thursday everyone!

      Wednesday, February 14, 2018

      Wednesday = Study!

      Tomorrow we will start class with a (10 minute quiz)--there are three questions:

      • Determine if a confidence interval is appropriate (know the name of this type of interval)
      • Interpret the meaning of a given interval
      • Identify the values of x, n, and p-hat for a given context
      To study you can complete the practice quiz provided below! I added two extra questions (in red) to better reflect tomorrow's quiz.


      Pop Practice Quiz! Context and Confidence Intervals!
      A Rutgers University study released in 2002 found that many high-school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once.
      1.       Identify the sample size and describe the sample from which we obtained our data. (2 points)
      2.       Define the population of interest. (2 points)
      3.       What is the population parameter of interest? That is, what (type of) value are you trying estimate (about the population)? (2 points)
      4.       Identify each of the following: (3 points)
         n = ___________                x = ___________          p-hat = ____________    

      5.       Verify that the conditions for a one-proportion z-interval are satisfied. BE DETAILED in your explanations! (6 points)         
      6.       Create a 98% confidence interval to estimate the proportion of high school students nationwide who have cheated at least once.
      7.       A 98% confidence interval was created to estimate the proportion of high school students nationwide who have cheated at least once. Interpret the meaning of this interval: (0.72479, 0.75521)



      And here are the answers to the practice quiz!
      1. Sample: 4500 high school students selected from across the nation
      2. Population of Interest: all high school students nationwide
      3. Parameter of Interest: % of all high school students nationwide who have cheated (on tests) at least once
      4. n = 4500, p-hat = 0.74 or 74%, x = (0.74)(4500) = 3330
      5. Researchers surveyed a random sample of 4500 high school students, 4500 is < 10% of all high school students nationwide, and (4500)(0.74)>10 and (4500)(1-0.74)>10; therefore, a one proportion z interval IS appopriate.
      6. Interval = (0.72479, 0.75521) (Use OnePropZInt on your calculator to get this)
      7. We are 98% confident that the true proportion of high school students nationwide who have cheated (on tests) at least once falls between 72.479% and 75.521% based on this sample of 4500 high school students.

      Tomorrow in class (after our 10 min quiz) it's all about the formula! I can't wait--see you there!

      Tuesday, February 13, 2018

      Tuesday HW!

      Today in class we looked a little more at the interpretations of confidence intervals and did a quick review of the conditions for a one proportion z-interval--these ideas will be assessed on our quiz to start class on Thursday; tonight's homework also gives us the opportunity to practice this stuff in preparation for that quiz.

      Tomorrow (and through the rest of the week) we'll start to explore the mathematics of confidence intervals, starting with an exploration of how we calculate a confidence interval.

      Tonight, please complete the following in your textbook, OR the questions are posted below:

      Page 447: 3a, 13abd, 11(just check conditions)

      3a.) Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems. They find that 14 of the 134 cars stopped have at least one safety violation. They want to estimate the percentage of all cars that may be unsafe (have at least one safety violation).

           1. Identify the population and the sample.
           2. Explain what p and p-hat represent.
           3. Determine if we can use a one proportion z interval (check conditions!)

      13.) An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.

      a.) Create a 95% confidence interval for the percentage of all auto accidents that involve teeenage drivers. Assume the conditions for inference have been satisfied.

      • To create the "one proportion z interval" we'll use our calculator...
      • Press STAT, scroll over to TESTS
      • Choose "OnePropZ-Int"
      • Enter x, n, and our confidence level.
      • Press calculate and you'll see your interval
      b.) Explain what your interval means. (Interpret your interval).

      d.) A politician urging tighter restrictions on drivers' license issued to teens says, "In one of every five auto accidents, a teenager is behind the wheel." Does your confidence interval support or contradict this statement? Explain.
      • Consider the interval from (a) and what that interval tells us (b)...does our interval suggest that in 1 of every 5 auto accidents a teenager is behind the wheel? Why or why not?
      11.) A May 2000 Gallup Poll found that 38% of a random sample of 1,012 adults said they believe in ghosts. This data was used to create a confidence interval to estimate the percent of American adults who believe in ghosts.

      Determine if a one proportion z interval is appropriate.


      Homework Answer Key:

      3a.) KEY

      • Population = "all cars" (in the US? in this state? who travel this road? This part is not clear.)
      • Sample = the 134 cars that were stopped and checked to see if they had at least one safety violation
      • p = the % of all cars that are "unsafe" (have at least one safety violation)
      • p-hat = the % of the 134 cars stopped that were deemed unsafe (p-hat = 14/134 = 0.1045 = 10.45%)
      • We CAN use a one proportion z interval because:
        • We will assume the 134 cars were selected randomly
        • 134 < 10% of all cars 
        • 134(0.1044) > 10 (or 14 >10) and 134(1-0.1044)>10 (or 120 >10)
      13.) KEY

      • 13a) 95% Confidence Interval: (0.12685, 0.18586)
      • 13b.) We are 95% confident that the true percentage of all auto accidents that involve teenage drivers falls between 12.685% and 18.586% based on this sample of 582 accidents.
      • 13c.) **Discuss as a class**
      11.) A one proportion z interval IS appropriate because:
      • The sample of 1,012 adults was selected randomly.
      • 1012 < 10% of all adults in the U.S.
      • 1012(0.38) > 10 and 1012(1 - 0.38) > 10