Failure to do so will be a grave injustice to math enthusistists everywhere!!!

Transcription

1 Tomorrow is Pi Day In order to honor Pi Day, we must prove the average measure of our circular objects is To do this...we must have the following items: circular plates (20) Circular cups (20) 12 cans/bottles of beverage (to be shared or 24) and hopefully one from each category: Cookies, pies, cake/ cup cakes, candy, Any food that is circular. Failure to do so will be a grave injustice to math enthusistists everywhere!!! 1

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4 3/14 AP STATS Warm up: Happy Pi Day! Please place all supplies on front or side table. EQ: How can you proof the value of PI using means? HW: Read Chapter 24 4

5 March 14, 2012 HW: None EQ: How can you proof the value of PI using means? Stats Pi DAY 1. Get in to groups of 2 or Create your Ho and Ha to show evidence that circular object are similar to We will pass out the objects for you to calculate the circumference and diameters of each. 4. Once all the calculations are done we will run the test. 5. After we show evidence that there is some truth to then we can eat the evidence. EATING BEFORE STEP 5 is an automatic F...no make ups. 5

6 Ho: Ha: Assumptions: Random: Nearly normal: Test performed: t score: Df: P value: Conclusion: Extension: Find the confidence interval at 90%. Is inside that interval? 6

7 3/15 AP STATS Warm up: Name an instance where you could use a t test. EQ: How does a 2 sample t test work? HW: HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 7

8 3/15/12 HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 Comparing two means: Notation Review: EQ: How does a 2 sample t test work? Chapter 24: Day 1 Typically used during experiments Population: μ, σ, SD Sample: y, s, SE Differences of means: Population: μ1 μ2 Observed Samples: 8

9 Previously: Standard deviations: If the data is independent and random, we can add the variances (σ 2 +σ 2 ) 1 2 Population: Sample: 9

10 2 Sample T Interval: ME= t * xse Confidence levels Calculator: Stats Tests 0: 2 samptint If you have the statistics: If you have a table of data: 10

11 Ex. 1) Using Data Battery life span in minutes L1= name brand L2= generic Find the interval that the battery lasts with 95% confidence. L1 (x) = L1 (s) = (, ) L2 (x) = L2 (s) = From these samples, with the confidence of %. The life span of name brand compared to generic brand will last from to. 11

12 Ex. 2) Using Data Core Plus Mathematics Project Background info: It was a study conducted to compare students using technology in Algebra to students who did not use technology. X1= X2= Confidence %= 90% P value: t score: df: (, ) Conclusion: 12

13 Two sample T test: H o and H A t score: ) More notation: Δo = delta naught or the difference of the means Calculator: Stats Test 4: 2 sampttest Sample below used battery data: Results: 13

14 Ex. 3) 2 sample t test using data: Camera Prices Gathering information...decide is there a difference in price if selling between friends and strangers? Ho: Ha: Sample 1: Friends Sample 2: Strangers n= 8 n= 7 x= $ x= $ s= $18.31 s= $46.43 Assumptions: Groups independent: Random: Nearly normal: T score: Df: p value: Conclusion: 14

15 Pooling revisited: When the variances are equivalent, you can pool the variances. AKA the range is the same. If done, this would be considered a pooled t test. Pros: simple degree of freedom formula n 1 + n 2 2 Cons: an extra assumption: Equal Variance Assumption: Is variance 1 σ 2 = variance 2 σ 2? To check without statistics, make a box plot. (box and whisker plot.) Calculator Review Using Battery Example: Stat edit put name in L1 and generic in L2. 2nd y= turn plot on and highlight boxplot. 15

16 Well, are they the same range? If you can't tell, change the window. Window Xscl 20 Pooling is optional. If not sure, don't use it. It doesn't change much. If you want more info. Read the book. 16

17 Last important item: df of two means lies between (n smaller 1) and (n 1 +n 2 2) The formula is on page 549. Summary: df= 17

18 3/16 AP STATS Warm up: What is pooling? EQ: Explain a paired T test? HW: HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 18

19 3/16/12 HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 Paired T test EQ: Explain a paired T test? Chapter 25: Day 2 Typically, one subject recorded in two separate occasions. The data is NOT independent of each other. Before and After situations (Think weight loss commercials) Data is collected on each subject and a difference is calculated. 19

20 Tips: If in an experiment, it's called "blocking". If it's an observational study, it's called "matched". Assumptions: Independence: No independence... Random: Please check...else we need to conclude that it's only valid for the sample given. 10% condition (is back): is it less than 10% of the focused population. Nearly normal: Are the differences normal? Again use a histogram if samples are smaller than

21 Ho/Ha: Same as previously mentioned... Ho: μd = Δo In other words...mean difference = 0 Ha: μd Δo or μd > Δo or μd < Δo Formulas: t n 1 = d Δo SE ( d ) where d bar = average pairwise difference SE ( d ) = s d n Margin of error (for confidence intervals) : d ± tn-1 x SE(d) 21

22 Ex. 4) Confidence interval: Exercise Average minutes women took to burn 200 calories. Run a confidence interval at 95% of how much longer it took women to work out at light exertion compared to hard exertion. 22

23 Ex. 5) Paired t test: Brakes A tire manufacture tested stopping distances for a specific tire model. To test the car made repeated stops after going speeds of 60 mph. The test was done on wet and dry land. Does the stopping distance vary between wet and dry. 23

24 In groups of 2, Grab a book...turn to page 583 Work through the 5 just checking questions. Due Monday. REMINDER ALL MAKE UP WORK DUE MONDAY! 24

25 3/19 AP STATS Warm up: What is 1 major difference between 2 sample t test and a paired t test? EQ: Explain a paired T test? HW: HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 Due Tuesday. 25

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28 3/20 AP STATS Warm up: Get out your review EQ: Explain a paired T test? HW: HW: Pg 566 #5, 8, 23, 32 Pg 586 #2, 7, 8, 11, 12 Due Tuesday. 28

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34 3/21 AP STATS Warm up: You have 8 minutes to review EQ: Explain a paired T test? HW: Read chapter 26 34

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