1. CHAPTER 10 DAY 1

2. Margin of Error The estimate is our guess for the value of the unknown parameter. The margin of error shows how accurate we believe our guess is, based on the variability of the estimate.

3. Confidence Interval Gives the estimate ± margin of error. And we can state this for a given percentage of confidence – which we will use a z-score chart for in this lesson!

4. Confidence Intervals Any confidence interval has two parts: an interval computed from the data and a confidence level giving the probability that the method produces an interval that covers the parameter. Usually the confidence interval is 90% or higher because we want to be quite sure of our conclusions.

5. Assume that 37% of all voting fans chose Ohio State to play in the National Championship game vs. Florida State with a ±6% error for 95% confidence. What is the confidence interval for the percent who believe that Ohio State belonged? What does this mean? We can say with 95% confidence that the true percentage of all fans is between 31%-43%

6. Confidence Interval To get confidence level C we want the central probability C under a normal curve. To do that, we must go out z* standard deviations on either side of the mean. The number z* is the same for any normal distribution.

7. Critical Values The number z* with a probability p lying to its right under the standard normal curve is called the upper p critical value of the standard normal distribution.

8. Confidence Interval To compute confidence intervals from a standard normal curve, we use a tail area… For a confidence level of 90%, tail area is.05 z* = 1.645 For a confidence level of 95%, tail area of.025 z* = 1.960 For a confidence level of 99%, tail area of.005 z* = 2.576

9. Confidence Interval for a Population Mean

10. Example Bob’s Pizza Shop averages µ pizzas on a Saturday evening. An SRS of 500 restaurants, σ = 8, averages 103 pizzas and is approximately normal. Determine a 95% confidence interval for µ.

11. Homework #5 The Degree of Reading Power (DRP) is a test of the reading ability of children. Use the DRP scores for 44 third-grade students in a suburban school district given. A. Make a stemplot of the distribution. B. Suppose that the standard deviation of the population of DRP scores is known to be σ = 11. Give a 99% confidence interval for the mean score in the school district.