1. Inference Chapter 9 Overview Unit 6 Intro

2. Inference Statistical inference is drawing conclusions about a population on the basis of data from a sample Notation: x = average of sample (statistic) μ = average of population (parameter) s = standard deviation of sample σ = (sigma) standard dev. of population μ = Greek Letter Muσ = Greek Letter Sigma

3. Inference: Using Data to Disprove a Claim The null hypothesis is the result needed to disprove the claim, H o The alternative hypothesis is the claim about the population we are trying to find evidence for, H a

4. Inference: Using Data to Disprove a Claim 1) Find the difference between your data and the claim. Subtract in such a way that you get a negative number. 2) Divide by the standard deviation. Treat this as your z-score. Look up the percentile in the z-table. Multiply the percentile by 2 This number you get is the percent likelihood that your data agrees with the claim

5. Practice: Categorical What percent of people do you think are left handed? 11% of 123 people surveyed in the class opening survey are left handed.

6. Practice: Quantitative What is the average height of Saint Joe upperclassmen? Of 127 peopled surveyed in the statistics class survey, the average height is 68.8 in. with a standard deviation of 4.8 in.

7. How Many Do You Need? For categorical data we’ve established that a 95% confidence interval may be calculated from: Maximum error occurs when p = 0.5 = 50% – If you don’t trust me, this can be proved with Calculus! Plugging 0.5 in for p this equation simplifies to

8. How Many Do You Need? Max error occurs at How many people should you interview to have a 95% confidence interval of 5%?

9. Prove It! Read Example 9.7 on page 439. – What are the odds of that outcome? What about claims that we can’t calculate the probability of? Next we’re going to go over how to use inference to see if a claim is true.