1. 3.07: Confidence Intervals 1 Goals of the lesson: introduce related vocabulary, develop understanding of point estimates and confidence intervals

2. The $100 question Imagine that Ms Cooper will pay you $100 if you can accurately predict how many calculators PAHS will need to buy for next year (and save money not getting extras) What would you need to know to make this prediction?

3. Collect Data Did you borrow a calculator in grade ten? Did you borrow a calculator for this course?

4. Consider the Data Is our data biased?

5. Consider the Data How accurate would it be to assume that our class results will be an accurate prediction for the entire school? Would you approach the problem differently if this were your full-time job and making an inaccurate prediction could get you fired?

6. Vocabulary Population – all the possible pieces of data for a particular question / problem Sample – a subset of pieces of data for a particular question / problem

7. Population vs Sample Making number-based statements about an entire population is difficult since it requires some kind of measurement of all data values Samples are smaller, often easier to collect data – we use samples to make inferences/predictions about the population

8. (In Future Stats Courses...) You will use different symbols for mean and standard deviation when discussing samples The formula for standard deviation is a little different for samples You will talk about different sampling methods and their pro’s and con’s (simple random, systematic, cluster, convenience, etc)

9. Population vs Sample Pick three numbers between 1 and 12 When the grid is un-covered, find the mean number of stars for your three selections Did everyone get the same mean? 1 = ***2 = **3 = ****4 = * 5 = ****6 = *7 = **8 = ***** 9 = **10 = ***11 = *12 = ***

10. Population vs Sample We assume that the population doesn’t change during the snapshot of time we consider it, so population μ and σ don’t change Since different samples can include different pieces of data, mean and std dev can be different from sample to sample

11. Predictions about the Population Predicting population μ is one of the most common tasks in statistics Sample mean will be closer if: – Population data is fairly uniform – Sample size is large compared to population size

12. Vocabulary Point estimate – a single value to estimate population μ

13. Vocabulary Interval estimate – an interval estimated to include population μ

14. Vocabulary A confidence interval is an example: – Point estimate plus/minus a margin of error, with a confidence level associated 68% of Math 11 students ±5% will go to university the year after high school, 19 times out of 20

15. Example The average high school student will send 58 text messages (± 12) during the school day, 9 times out of 10. The point estimate is The margin of error is The confidence level is

16. Example A typical Canadian wedding costs between $10 000 and $10 800, 99 times out of 100. The point estimate is The margin of error is The confidence level is

17. Visualizing Confidence Intervals Population μ = 12 Interval 1: 8 to 14 Interval 2: 11 to 15 Interval 3: 13 to 14 Interval 4: 10 to 12

18. Visualizing Confidence Intervals

20. Changing the Size of the Interval Intervals will be smaller/narrower if: – sample data is more uniform – sample size is larger – confidence level is lower

21. Example One study finds that the average human pregnancy lasts 280 days, ± 10 days, for 70% of all pregnancies. What is the margin of error? What is the confidence interval?

22. Applying Confidence intervals

24. Example 2:

28. Homework page 274 # 1 2 3 Pages 280-282 # 1-12