Confidence Intervals

Transcription

1 Confidence Intervals MGSE9 12.S.IC.4 Use data from a sample survey to estimate a population mean or proportion develop a margin of error through the use of simulation models for random sampling. Jan 28 8:08 AM Vocabulary Confidence Interval based on a sample, a range of values based in which we can say the population mean will fall with a given % certainty. The correct mean will be captured in that % of sample intervals. Oct 28 3:17 PM 1

2 What am I learning today? How to use a sample mean to predict the population mean. How will I show that I learned it? Create confidence intervals of a given % from the results of a sample. Aug 18 1:21 PM Confidence Interval From a sample mean, we are trying to find the population mean ( ) using the CLT. We can do so with a certain level of confidence by using our sample mean, standard deviation of sample means, and the z score for the desired confidence percentage. Jan 13 3:53 PM 2

3 Necessary for Confidence Intervals 1. A sample whose size is n 30 (preferred for our z-score calculation). 2. The mean of the sample. 3. The standard deviation of the population. 4. The confidence percentage that we want to calculate. Jan 13 3:53 PM Common Z Scores The C.I. % indicates the percent symmetrically taken from the mean out. For instance, if I want a 80% CI, I will cut off 20%/2 = 10% from each side. Z Score = Jan 18 8:47 PM 3

4 The admissions director at Wheeler Magnet has a novel idea. She wants to use the PSAT scores of current students as a marketing tool for other Cobb students. She has enough money to evaluate 50 students scores. The director picks a SRS (simple random sample) of 50 students to evaluate their scores. The mean PSAT score for the sample is 156. The standard deviation of the most recent PSAT was 33. What can the director say about the mean score μ of the population with 95% confidence? Step 1: Calculate the standard deviation of the sample. Step 2: Use the confidence interval you want and the z-score to determine a margin of error. Step 3: Use your sample population and your margin of error to write an interval. The admissions director at Wheeler Magnet has a novel idea. She wants to use the PSAT scores of current students as a marketing tool for other Cobb students. She has enough money to evaluate 50 students scores. The director picks a SRS (simple random sample) of 50 students to evaluate their scores. The mean PSAT score for the sample is 156. The standard deviation of the most recent PSAT was 33. What can the director say about the mean score μ of the population with 95% confidence? If I wanted an 80% confidence interval, how would that have changed my calculation? 4

5 The new insurance agent for a large company wants to know the average blood pressure of the company s employees to help calculate their risk. She has enough money to take a SRS of 35 employees. Their mean diastolic pressure is 83. The standard deviation for diastolic pressure is 9.7 nationwide. What is the 90% confidence interval for the company s population mean for diastolic pressure? What is the 95% confidence interval for the company s population mean for diastolic pressure? What is the 99% confidence interval for the company s population mean for diastolic pressure? What happens to your confidence intervals as you want to be more confident? The new insurance agent for a large company wants to know the average blood pressure of the company s employees to help calculate their risk. She has enough money to take a SRS of 35 employees. Their mean diastolic pressure is 83. The standard deviation for diastolic pressure is 9.7 nationwide. If you wanted a 99% confidence interval whose width is no greater than 40 points, what sample size would you need? 5