You Completed AP Stat!

You did it! We learned a lot this year; we worked super hard and did lots of homework; the AP exam and the final exam have both come and gone; and for many of us, we're thinking about the next major chapter of our lives as graduation approaches!

Thank you all for an amazing year! I appreciate all of your hard work and I am extremely proud of all we have accomplished! Check back for a blog post in July for some data about our AP exam performance!

Seniors--I wish you the best of luck! Come back and visit sometime!

Underclassmen--Same to you! Come visit in 101! I look forward to seeing you in the halls next year!

Everyone have an amazing summer! Rest up, relax, have LOTS of FUN with friends and family, and start your next year strong!

Until then, here are some interesting articles you can check out when you get bored!

There's A Mathematical Reason You Are Less Popular Than Your Friends...

20 Signs Your'e A Math Major

Ace Our Final!

If you're going to the prom tonight, HAVE FUN! Enjoy the night and be safe! Don't do anything I wouldn't do! :)

Take advantage of an "aceable" exam! No matter what your grade was or what grade you're in, end strong! Don't blow this off! If you put in the effort you can definitely get an A or a B on this test! So do it!

To those of you who are exempt, congratulations on a great year of AP Stat! You should be super proud of yourself! You will definitely be missed in class though!

In case you lost your review packet, here's what's on our final! See you there!

I.                    Format:

a.       100 Multiple Choice

II.                  Practice Questions (answers are shown in parentheses):

1. Students were asked for the number of hours they spend listening to music in one 7-day week. Their responses are shown below:

3,  0.5,  7,  10,  3.5,  4,  4,  5,  2,  2,  1,  0,  0.5,  6, 5

1.      Calculate each of the following:

a.      Mean (3.57)

b.      Standard Deviation (2.76)

c.       Sample Size (15)

d.      Median (3.5)

e.      Minimum (0)

f.        Maximum (10)

g.      Range (10)

h.      Q1/25^th Percentile (1)

i.        Q3/75^th Percentile (5)

j.        Interquartile Range (4)

k.       Mode (4, 2, or 0.5)

l.        Type of Study (Experiment, Observational Study, or Survey?)

m.    What percent of values fall below 6? (12/15 = 75%)

n.      What percent of values fall above 4? (5/15 = 33.33%)

o.      Midrange (5)

p.      If each number were tripled, the new median would be...(10.5)

q.      If each number were tripled, the new range would be…(30)

r.       If we added 2 hours to each value above, the new median would be…(5.5)

s.       If we added 2 hours to each value above, the new range would be…(10)

t.        What is the percentile for a student who listens to 3.5 hours of music? (7/15 = 46.67%)

2.     
A spinner has four equal size sections, red, blue, yellow, and green. Each spin is independent of the next.

a.      What is the probability of spinning a red? (0.25)

b.      What is the probability of spinning 5 consecutive reds? (0.00098)

c.       The probability the spinner lands on a color is…(1)

d.      The probability the spinner lands on orange is…(0)

e.      A person spins and lands on blue 10 consecutive times. What is the probability the next spin is also blue? (0.25)

f.        What is the probability of landing on blue or green? (0.5)

g.      What is the probability the spinner does not land on green? (0.75)

3.      General Statistics Info…

a.      List all measures of center for quantitative data.

b.      List all measures of spread for quantitative data.

c.       List all descriptions of “shape” for a histogram of quantitative data.

d.      If a histogram is skewed left, how does the mean compare to the median?

e.      If a histogram is skewed right, how does the mean compare to the median?

f.        If a histogram is symmetric, how does the mean compare to the median?

g.      A p-value of 0.000000019 would lead us to what conclusion? (reject the null hypothesis, fail to reject, etc.)

h.      A p-value of 0.50 would lead us to what conclusion?

i.        What are the different types of samples?

j.        What are the (names of) statistical tests we’ve investigated in class?

k.       What is the shape of a Normal model?

l.        What is the shape of the (Student’s) t-distribution? Compare to the Normal model.

m.     What is the shape of the Chi-Squared distribution?

n.      What types of graphs are used for quantitative data?

o.      What types of graphs are used for categorical data?

p.      What is the Area Principle?

q.      What are the types of error? Define each.

r.       What is correlation?

s.       What values can the correlation take on? (What are its max/min?)

4. The data set below shows the number of AP classes students took (x) versus their class rank (y):

AP Classes	5	3	2	2	1	0	4	5
Rank	8	14	18	20	23	29	11	6

a.      What is the correlation for this data set? (-0.99)

b.      What is the slope of this regression? (-4.24)

c.       What is the y-intercept of this regression? (27.8)

d.      What is the value of the Coefficient of Determination? (98.27%)

e.      Use the equation of the LSRL to predict the class rank for a student who takes 6 AP classes.

a.      The student with 6 AP classes had a class rank of 24. Find the residual for this prediction.

5. Who are some statisticians we’ve come across (or maybe didn’t…) throughout our course?

Additional Topics on the Final Exam:

·         Calculating a z-score

o   Comparing z-scores to see which is more “unusual”

o   What is an “unusual” z-score?

·         Estimate a correlation given a scatter plot

·         Describe the shape of a distribution given a graph

·         Know our tools for inference and what they are used for

o   We use confidence intervals to estimate a parameter

o   We use hypothesis tests to determine if a parameter has significantly increased/decreased/changed

·         Hypotheses…

o   Which hypothesis do we assume to be true?

o   Which hypothesis shows what we are trying to prove?

·         Bias…what is it?

·         Identify a method of data collection (from context)

o   Simulations, Surveys, Experiments, and Observational Studies

·         Find expected value given a probability distribution

·         Identify the sample size (n) given a context

·         Name different graphical displays and know which types of data they are used for

·         Venn Diagram probability problems

o   Suppose 40% of students at a local school play soccer, 50% play basketball, and 25% play both.

o   What % play only soccer? What % play only basketball? What % play basketball or soccer? What % play neither sport?

·         Definitions of Type 1 and Type 2 Error

o   Which is a false positive? False negative?

·         Find the fences given the 5 number summary

o   Use these fences to determine if there are outliers in a data set

·         Know the 68/95/99.7 rule (also called the Empirical rule)

o   Draw/label a Normal model using this rule

·         Know the general process for a confidence interval or hypothesis test

o   Confidence Interval: conditions, math/formula, interpret

o   Hypothesis Test: hypotheses, conditions, math (z or t score, p-value), conclusion

·         P-Values

o   What do we use them for?

o   If the p-value is below alpha….

o   If the p-value is great than alpha…

o   If we reject the null, there _________ evidence of the Ha (is or is not?)

o   If we fail to reject the null, there ) _________ evidence of the Ha (is or is not?)

Last Week of Classes

Here are the things you need to keep in mind:

• Get your textbooks (and graphing calculators) in! I'm going to start writing accountabilities Thursday/Friday!
• The crossword puzzles (extra credit homework) are due by Thurdsay! No later!
• STAMPS ARE DUE THURSDAY! Start counting them up now so you're ready to turn them in!
• Write your name and the total on the front!
• Double check!
• You are literally counting the number of stamps!

And lastly, math people, check out this interesting article about the Fourier Transform!

Happy Memorial Day!

This weekend, no homework of course--unless you want to do some extra credit!

Here are the things you need to keep in mind:

• Get your textbooks (and graphing calculators) in! I'm going to start writing accountabilities next week!
• If you would like to get some homework extra credit (fill in 2 past homework zeros) then you must turn in the crossword puzzles (one or both) by Thursday!
• Stamps are due next week (Thursday/Friday)! Start counting them up now so you're ready to turn them in!

And here's the plan for next week:

• Tuesday: more ancient number systems!
• Wednesday: final exam review packet: groupwork
• Thursday: final exam review game! 
• After working on the review packet on Tuesday I will put you into random groups on Wednesday...
• I will then generate random names; if the person whose name comes up can tell me the answer to the review question and/or how to do it, then that person's group gets a point!
• If someone copies an answer from a neighbor, that group will lose points! Multiple instances of cheating = disqualification!
• The group with the most points wins! (candy!)
• Friday: do some brainteasers for a couple last minute stamps, answer any last final exam questions, reflect on our year of hard work!.

Enjoy the weekend! For many of you, this is your last long weekend of your high school career! Whaaaatttttt!!!????

Happy Thursday!

Tomorrow in class we'll wrap up our Blackjack/Counting Cards "mini unit" with one last Numb3rs episode regarding the topic.

Then, on Tuesday/Wednesday we'll do some final exam review (and talk about the exam). We'll finish up with one last assignment on Thursday/Friday--see you there!

Two things to remember:

• Stamps are due next week! Start counting them up!
• Get your textbooks/calculators in! I'm starting to write accountabilities next week!

We're almost there! Stay focused and finish strong!

Monday/Tuesday/Wednesday....

Happy Monday! For the seniors, this is your last Monday of high school classes! (We have one more Monday, exam day)

Today in class we finished 21 and took our quiz! If you were out today you will have to make up this quiz on Thursday or Friday in class! Be responsible and finish your notes!

Here's an outline of the week's plan....

• Monday: finished 21, took 21/blackjack quiz (must be made up by the end of the week if you were out)
• Tuesday: sub work! Read the provided article and turn in the questions. This MUST be completed in class and turned in to the sub for credit!
• Wednesday: Senior picnic! Our classes will be pretty small, so we'll watch an awesome Numb3rs episode on this day!
• Thursday/Friday: Last classwork grade (other than stamps)! We will have another article ("Fighting Crime with Statistics 101) to read, followed by some more questions! We will work on this in class on Thursday and Friday!

Enjoy your Monday, Tuesday, and Wednesday if I don't see you! Have a blast at the senior picnic if you're there!

21: The movie, the game, and card counting...

Please return your textbooks and graphing calculators ASAP!

Everyone will be taking the quiz on 21, blackjack, and card counting on Monday--so if you were out, it is your responsibility to find/watch this movie (this weekend), and/or to watch the youtube videos linked below to learn about card counting and blackjack! Do some Googling and you should be able to find a site where you can stream the movie for free! If you do find a link to stream the movie, please email it to me so I can post it on the blog! (carofano.fm@easthartford.org).

Remember, you can use any notes you take on your quiz! (But only YOUR notes!)

And lastly, if you took either/both of the makeup homework assignments today, you MUST turn these in by MONDAY! No late papers will be accepted! Yes, these are actually difficult AP Stat problems--but you're trying to make up missing AP Stat homework, so it's only fair! You must provide quality, correct work to earn the homework credit! Lazy responses will simply be discarded!

Here are some links to videos explaining the basics of Blackjack (21) and Card Counting!

• Blackjack Basics

• How to Play Blackjack! 

• Blackjack: Basic Strategy (we didn't see this in class!) 

• Card Counting Basics 

• Card Counting Explained by Jeffery Ma (the guy this movie is based on)

And here are some more links...a video explaining the "Monty Hall Problem" (the one with the cars and goats that appears in class):

• The Monty Hall Problem: Scene from 21! 

• The Monty Hall Problem Explained: ASAPScience  

• The Monty Hall Problem Explained with a Tree Diagram!

Otherwise...check this out! Here's a short article about being an Environmental Statistician for those of you who love science and love Statistics!

• Why Should I Become an Environmental Statistician?