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%)