CLT video

http://gallery.me.com/mrmathman/100124

This should help you think about the Central Limit Theorem

t and X^2 review

Name the procedure:
Page 574 #4a, 6, 7, 10, 12, 23, 27, 30acd

practice, practice

Ch. 26 #5, 6, 10, 14
The X^2 for the evens are:  3.677, 290.131, 479.508 (listed in no particular order!).  But that lets you check your work, at least a little bit!

2-way table

Ch. 26 #12 & 13

More G of Fit

Ch. 26 #4, 7, 8

G of fit!

Ch. 26 #2

2-t (and some not!)

Ch. 24 #9, 14 and 16

matched pairs

Ch. 25 #14

tests and intervals together!

Ch. 23 #28, 29

Ch. 13 #35

t-tests

Ch. 23 #17, 21, 25

t-intervals

Ch. 23 #13 & 23

Due on Friday

Read and answer!
statsarticles.blogspot.com

Review!

Page 437 #2, 5, 27, 29, 30
Due Wednesday!
No Late Work!!

Chapter 21 recap

Sample Size!
The bigger the sample size, the more power we have.
We also lower our chances of making either error.

More Sample Size!
We need to be careful with REALLY big sample sizes.
The standard deviation gets really small and you'll always get a small p-value.
This can cloud practical significance: use a confidence interval instead!

Ho is false!
If the Ho is really false, we have lots of power and very little Type
II error (dumb criminal).
If the true value differs only slightly from the Ho, we have little
power and may make a Type II error. (smart criminal)
This is called effect size.

Changing alpha
Making alpha smaller (0.01) makes it harder to reject.
We do this if want less Type I, but are willing to tolerate more Type
II and less power.
i.e., death penalty

Alpha and medicine
If the established treatment is highly effective, you demand a very
small p-value before rejecting (low alpha).
If the standard treatment is not very effective and you have reason to
believe it can be easily improved, you would be more willing to accept
a new treatment even though the p-value is larger (higher alpha).

website

Want to play around with the web site I showed you Thursday?

http://wise.cgu.edu/power/powerapplet1.html

Enjoy!

error?

Ch. 21 #5, 11, 12 (skip e)

quest tomorrow

Ch. 20 #21, 23 + 90% confidence interval for both

sub work

Ch. 20 #2, 7, 8, 18, 19

Tests!

Ch. 20 #9

sample size?

Ch. 19 #3, 8, 13, 25bc

Enjoy!!

End of 18

Ch. 18 #15, 16, 27, 27

Ch. 6 #25e, 27c

p-hats

Ch. 18 #12-14

proportions

Ch. 18 #7, 9, 11

Finals!

An easier simulation is:
Ch. 11 #19
You could look back on old homework, too (Chapter 11)

If you get totally stuck, send me an email, I'll send some answers.

Binomial practice

Ch. 17 #13-21 odd

more review

Page 342 #20, 25, 26

Probability review

Page 340 #1, 2, 5, 15, 16, 19, 20

the end...

Ch. 17 #19ab, #21a

Binomial

Ch. 17 #14abd
Page 341 #3, 6, 7
Merry Christmas!

Binomial

Ch. 16 #33
Ch. 17 #6

Tuesday's work

Ch. 16 #5, 6 and 14

rules, rules

Ch. 16 #25, 27, 30

14 and 15

Ch. 14 #20, 21
Ch. 15 #23, 24, 17

Last night: Ch. 15 #4, 14, 20

End of Unit 3

Page 269 #23, 24, 29

Chapter 13

#23-26

more experiments

Ch. 13 #28, 29, 30

Experiments!

Ch. 13 #6-8

End of 12

Ch. 12 #8, 9, 18, 19, 22

just a bit

Find a price from your parents and figure out the inflation rate
Finish #4: graph and algebra
On the ball lab: are the graphs continuous or discrete? what are the
y-intercepts?

methods

Ch. 12 #11, 12, 14

survey says...

Ch. 12 #5-8
Read P. 241-242

Unit 2 Review

Ch. 10 #27
Unit II Review #1, 2, 4, 8, 9, 37, 40
Due Wednesday!
Article Due Friday!!

more transformations

worksheet

transformers!

Ch. 10 #1, 2, 7

Influential

Ch. 9 #11, 12, 13

end of chapter 8

HW:  Ch. 8 #31, 32, 36

Notes from today in class:

• What the heck is a "line of best fit"?
  
• Its real name is: Least Squares Regression Line!
  
• Or:  LSRL
  
• Least squares? least squares of what?
  
• The sum of all the residuals squared is as small as possible!
  
• Regression?  What does that word mean?
  
• r tells us how much to regress to the mean (example…)
  
• And speaking of mean:
  
• (x-bar, y-bar) is on the line (duh!).
  
• And btw:  the residuals always add up to zero.
• You should also note that if you switch x and y, the correlation does not change, but the LSRL does.
• You should never use a LSRL to predict x using y.  It is not created to minimize the predictions for x, only for y.

R^2

Ch. 8 #3bcd and #21

residuals

Ch 8 # 9c, 10de, 35d
Thanks!

slope, y-int

Ch. 8 #9ab, 10abc, 35abc

sofa

Ch. 7 #2, 6 & 8

Powerpoint flashcards

Hey all! Happy studying! Those flashcards we did today can be viewed at:

http://gallery.me.com/mrmathman#100072

A good answer from the quiz:

The boys collected more candy with a higher median (62) than the girls (45.5).
Both the boys and girls have an IQR of 25, so their spreads are similar.
The boys were skewed left and the girls were symmetrical.

Unit 1 review

P. 105 # 5, 21, 25abcd, 27, 29, 31, 32
This is a review of everything so far this year.
Due Monday

Article #2
statsarticles.blogspot.com
Due Tuesday

Test will be Wednesday

Normal cdf

Ch. 6 #25abc, 26abc, 27a

normal!

Ch. 6 #7, 11

ogives!

WS: #30 and 1.20ab
Ch. 6 #2, 3

standard deviation

Ch. 5 #6, 21, 26, 36, 41

Outlier test

Ch. 5 #12bcd, 14, 15, 23b

boxplots

Ch. 5 #23cd, 35b + boxplot

Stem and leaf!

Ch. 4 #12, 17 & 24
Article #1
statsarticles.blogspot.com

Histograms

Ch. 3 #23
Ch. 4 #8, 18
Article #1 due Friday!

CUSS!

Ch. 4 #3 & 5

Independent?

Ch. 3 #15, 16 & 18
Friday's work: worksheet
All of this is due Tuesday.
And don't forget your die!
And the syllabus quiz!

Pie and bar

Ch. 2 #6
Ch. 3 #6, 8

Chapter 2!!

#2-5, that's it!

First day!

Read the syllabus:  quiz Friday.
Read chapter one:  quiz tomorrow!
Start making your die:  due next Tuesday.

first day of school!

HW:  Read the syllabus and chapter 1.

Test day

My civic duty is complete.  I'll be at school all day.  Feel free to come by before noon to say hi.  I'll come by the MPR before you start.  If you're studying tonight and want to e-mail a question, feel free.

Carne Asada Feast:  May 31!!!

sunday night

well, you're probably studying hard now.  I definitely have to go do my civic duty at jury duty tomorrow.  If there's anything that is stressing you out, feel free to drop me an e-mail!

mr d

O-6

OK, folks. O-6 will challenge you. Here's the answers:

a) Ho: p = 0.5; Ha: p=/ 0.5

b) Conditions for a 1-prop z-test are NOT satisfied, because 8*0.5 = 4 which is a lot less than 10. In other words, the expected number of successes is too small.

c) To work around this problem, we use binomial pdf. We use p = 0.5, n = 8 and fill in the table:

0 0.00391
1 0.03125
2 0.10937
3 0.21875
4 0.27344
5 0.21875
6 0.10937
7 0.03125
8 0.00391

d) Since the test is two-sided, we see this this:

If x = 0 or 8, p = 2*0.0391 which is less than 5%
If x <= 1, then we add up the lower 2 and upper 2 and get 0.07312, which is greater than 5%
So 5% is not possible.

e) For the provided data, x = 2. So the p-value is 2*P(x <= 2) = 2*(0.003906 + 0.03125 + 0.109375) = 28.9% We would fail to reject and fail to find evidence of any difference between the two brands.

f) Increase sample size! It lowers the expected sd and enables us to more clearly see any differences that might exist between the two brands. sqrt(p*1-p/n) gets smaller!

That's a doozy of a problem, but hopefully this helps!

More??

OK folks, here's what I've done:

• Flashcards powerpoint
• Name that green sheet website
• Answers to test O
• Name that green sheet answers for tests I through Q

Keep scrolling down and you'll see all of that.

I'm more than happy to do more, but I will now switch to waiting for e-mail requests. I you want more answers (P or Q) or something else, just send me an e-mail:

mrmathman@(no-spam)gmail.com

Obviously, take out the no spam thing.

I'm more than happy to type up more answers if you're working hard and want them. Just drop me that e-mail and I'll put them up.

Good luck and happy studying to all!

Flashcards

I put the entire flashcard powerpoint here:

http://gallery.mac.com/mrmathman#100034

Enjoy!

web site for inference

This web site loads slowly, but is pretty nifty:

 

http://www.ltcconline.net/greenl/java/Statistics/StatsMatch/StatsMatch.htm

 

Note: the wording on this website is more vague than the AP test. The AP test always asks for "a 95% confidence interval" if it wants an interval (or some other %). Also, the AP problems are longer, and thus have more information that will guide you to deciding what to do.

However, I think that after you 10 or so of these, you'll get used to the wording of this site and it will be good practice. If it is just always frustrating, switch to finding the tests and intervals in your notebook. Every released test (A, B, C,...) has at least one.

Note: this website includes prediction intervals, which you do not need to know.

Answers for O #1-5

O-1a) 40% of the sales agents had sales of $300,000 or less.

O-1b) 10% (show work!)

O-1c) No agents had sales between $1 million and $1.1 million

O-1d) $800,000 (with explanation!)

O-2a) 2-prop z-interval (name or formula)

success = 188, 180 > 10

failures = 12, 20 > 10

Independent samples

(-0.0156, 0.0956)

We are 96% confident that the difference in the proportions of parts meeting specs for the two shifts is between -0.0156 and 0.0956.

O-2b) No, because 0 is in the interval, zero is a possible value. So we are 96% confident that zero difference in shift specs is possible. We make this decision using alpha = 0.04!!

O-3a) z > 1.14 = 12.71%

O-3b) 1 - (8729)^5

O-3c) invnorm(0.99) = 2.33

algebra: (291.2 - M)/2.8 = 2.33

M =

Show work!!!

O-4): matched pairs t-test

Ho: mu = 0

Ha: mu > 0 (mean diff (after - before) is greater than 0)

Name or formula: t = (x-bar - 0)/(s/sqrt(n))

SRS and graph to check nearly normal

t = 3.75

df = 11

p-value = 0.002

Reject Ho. Is evidence that people who complete program have increased dexterity.

O-5a)

rv: amount of draft

treatments: standard hitch and new hitch

experimental units: 2 large plots of land

O-5b)

Yes, the hitches are randomly assigned to the plots.

O-5c)

No. Each treatment was applied to only one plot. Replication is needed.

O-5d)

Even though 25 measurements were taken, each hitch was used on only one plot only. If a difference in the draft is observed, we will not know whether the difference is due to the hitch or the plot. The treatment (hitches) are confounded with the plots.

Name that green sheet

I-5c:  Chi-square goodness of fit

J-5:  Chi-sq 2-way table or 2-prop z

K-4:  2-mean t-interval

L-4:  1-prop z-test

M-4:  mp's 1-mean t-interval

N-4:  2-prop z interval

O-2:  2-prop z interval

O-4:  mp's 1 mean test

P-4:  mp's 1 mean t test

Q-5:  2-mean t test

Calendar info

Below you see the link for the review calendar. Please note:

**Click on "Week" to view a week at a time and better see the details
of what we did each day.

**Homework and classwork is listed for each day.

I hope this is helpful!

Review Calendar

To see a schedule of what we are going to review when, go to:

http://www.google.com/calendar/embed?src=5dskgriao5era1dj6un4ipgo7c%40group.calendar.google.com&ctz=America/Los_Angeles

Quest on Thursday

Last section of the book, aka, Unit VII Review: #10

2-way tables!!

Ch. 26 #12 and 13 (skip part a)

Goodness of fit

Ch. 26 #2 & 8

#6 is even? OK...

#6
69 and 103 > 10

69/172 +/- 1.96*sqrt(.401*.599/172)

I am 95% confident that the true percentage of Adirondack streams that
have a shale substrate is between 32.8% and 47.4%.

a few answers

#8:
histogram looks very nice and normal! (did you draw it?)

7.963 +/- (t*)(8.79/sqrt(27))
t* is for 26 df

I am 95% confident that the true mean difference between boys and
girls who have been drunk at least twice is between 4.5% and 11.4%

#10a)
1772/2000 = 88.6%

b) 250000/304266 = 82.2%

c) Type I = certify the petition when there are not enough sigs.

d) Type II = valid petition not certified.

e) Ho: p = 82.2% Ha: p > 82.2%

1772 and 228 > 10 check!

z = (.886 - .822)/0.008553

Note: use 0.822 in sd formula

z = 7.48, p-value = 0

We reject and say we found sig evidence that the % is greater than
82.%. Certify!

f) To increase power, collect even more sigs. Although it seems like
we have plenty of power.

#16
SRS
2 independent years
260, 240, 270 and 230 are all > 10

(0.54 - 0.52) +/- 1.96*sqrt( (.54*.46/500) + (.52*.48/500) )

I am 95% confident that the change in proportion of students who
choose to enroll is between -4.2% and 8.2%

16b) Since zero is in the interval, we would think that there is not
evidence of a change.

Test coming!

Page 510 and following: #5-10, 13, 16 19, 27
NAME them all.
Do three.

Read page 508

Organize

Today's assignment is to make a 4-quadrant graphic organizer that sorts all the information about the 4 different inference procedures.

Tuesday, March 4th

Ch 24 #8, 12, 23, 24

2-t!

Ch. 24 #7 and 9

2 samples, coming at ya!

Friday Article #9 is due!

test ideas

CLT?  Do Ch. 18 #21 and 23
1-mean?  Ch. 23 #21
matched pairs mean? Ch. 25 #14abc is great
Alpha?  Ch. 21 #11
Read?  "What Can Go Wrong?" on p. 415 and pages 444 and 445 (beer!)

t-test Thursday!!

Ch. 25 #14abc

Ch. 18 #24 and 28

matched pairs

Ch. 21 #14

Ch. 23 #24 interval and test

Ch. 25 #7 and 11

t from data

Ch. 23 #23:  test and interval

Class data:  test and interval

t-test

Ch. 23 #8, 9, 12, 22

Mr t, beer and mermaids

Ch. 23 #15

Note:  you'll need to use t* for 60, even though that isn't quite right...

Bonus reminder

Can you calculate sample size?

Here comes a test!

We did a crossword today:  study the vocabulary in chapters 19, 20 and 21.

 

The test:

Multiple Choice (study Ch. 19 #7 & 8 and...?)

A green sheet

Type I and II errors (study Ch. 21 #7 & 8)

Outlier test!!!!

 

Good luck!

alpha

HW:  Ch. 20 #22, Ch. 21 #9 and 10

Good review for Friday's test

HW:  Ch. 19 #26b, Ch. 20 #20, Ch. 21 #6-8

Quest tomorrow!

Ch. 19 #21
Ch. 20 #21

no homework

Quest on Friday
You might want to work on perfecting your homework and getting ready
for your Quest!

got behind, sorry...

Friday:  Ch. 20 #9 and 10

Monday:  Ch. 20 #11 (put a confidence interval and test on one green sheet)

Tuesday:  Ch. 20 #12 (in class) #13 and 14 (just check conditions) #15 & 16 (add a confidence interval on the bottom)