Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Degrees of freedom (statistics) wikipedia , lookup
Sufficient statistic wikipedia , lookup
Foundations of statistics wikipedia , lookup
History of statistics wikipedia , lookup
Taylor's law wikipedia , lookup
Bootstrapping (statistics) wikipedia , lookup
German tank problem wikipedia , lookup
Student's t-test wikipedia , lookup
Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE Confidence Intervals: A _____________________ is a statistic that provides an estimate of a population parameter. The value of that statistic from a sample is called a _______________________. Ideally, a _________________ is our ____________________ at the value of an unknown parameter. A Confidence interval for a population characteristic is an ________ of ________________for the characteristic. It is constructed so that, with a chosen ______________ of _______, the value of the characteristic will be ___________ inside the _______. Formula for Confidence Interval: Margin of error: 3 ways to make Margin of error smaller: Confidence Level: Interpretations (2 different ways ) What are 3 things you should NOT say? What are the conditions required to construct a Confidence Interval? Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE SOME COMMON CONFIDENCE LEVELS AND THEIR z* VALUES 1. Confidence level 90% 2. Confidence level 95% 3. Confidence level 99% Other z* values can be found STEPS IN CONSTRUCTING A CONFIDENCE INTERVAL. 1. 2. 3. 4. 5. One-Sample z interval for a Population Proportion. When the standard deviation of a statistic is estimated from data, the result is called the _______________________ of the statistic. Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE Example: The Gallup Youth Survey asked a random sample of 439 U.S. teens aged 13 to 17 whether they thought young people should wait to have sex until marriage. Of the sample, 246 said “Yes”. Construct and interpret a 95% confidence interval for the proportion of all teens who would say “Yes” if asked this question. Example: The present packaging system produces 10% defective cereal boxes. Using a new system, a random sample of 200 boxes had 11 defects. Does the new system produce fewer defects? Construct a confidence interval to answer this question. Sample Size for Desired Margin of Error Example: A company has received complaints about its customer service. The managers intend to hire a consultant to carry out a survey of customers. Before contacting the consultant, the company president wants some idea of the sample size that she will be required to pay for. One critical question is the degree of satisfaction with the company’s customer service, measure on a five-point scale. The president wants to estimate the proportion p of customers who are satisfied (that is, who choose either “satisfied” or “very satisfied,” the two highest levels on the fivepoint scale). She decides that she wants the estimate to be within 3% at a 95% confidence level. How large a sample is needed? SUMMARY/QUESTIONS TO ASK IN CLASS Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE One Sample z interval for a Population Mean Example: A random sample of the SAT math scores of 500 California high school students yields a mean of 461. We know that the standard deviation for all seniors is 100. Construct a 95% confidence interval for the mean of all California students. Comment on the meaning of this interval. Example: A test for the level of potassium in the blood is not perfectly precise. Suppose that repeated measurements for the same person on different days vary normally with s = 0.2. A random sample of three has a mean of 3.2. What is a 90% confidence interval for the mean potassium level Choosing the Sample Size Example: The heights of HH male students is normally distributed with s = 2.5 inches. How large a sample is necessary to be accurate within + .75 inches with a 95% confidence interval? SUMMARY/QUESTIONS TO ASK IN CLASS Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE The t Distributions When the of a statistic is estimated from the data, the result is called the of the statistic, and is given by . When we use this estimator, the statistic that results does not have a normal distribution, instead it has a new distribution, called the . The variability of the t-statistic is controlled by the . The number of is equal to . ASSUMING NORMALITY? USING THE t PROCEDURES 1. 2. 3. 4. SUMMARY/QUESTIONS TO ASK IN CLASS Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE Example: A manufacturer of high-resolution video terminals must control the tension on the mesh of fine wires that lies behind the surface of the viewing screen. Too much tension will tear the mesh, and too little will allow wrinkles. The tension is measured by an electrical device with output readings in millivolts (mV). Some variation is inherent in the production process. Here are the tension readings from a random sample of 20 screens from a single day’s production: Construct and interpret a 90% confidence interval for the mean tension μ of all the screens produced on this day. Environmentalists, government officials, and vehicle manufacturers are all interested in studying the auto exhaust emissions produced by motor vehicles. The major pollutants in auto exhaust from gasoline engines are hydrocarbons, carbon monoxide, and nitrogen oxides (NOX). Researchers collected data on the NOX levels (in grams/mile) for a random sample of 40 light-duty engines of the same type. The mean NOX reading was 1.2675 and the standard deviation was 0.3332. (a) Construct and interpret a 95% confidence interval for the mean amount of NOX emitted by light-duty engines of this type. (b) The environmental Protection Agency (EPA) sets a limit of 1.0 gram/mile for NOX emissions. Are you convinced that this type of engine has a mean NOX level of 1.0 or less? Use your interval from (a) to support your answer. SUMMARY/QUESTIONS TO ASK IN CLASS Name _______________________________ AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE Example : The times of first sprinkler activation (seconds) for a series of fire-prevention sprinklers were as follows: 27 30 24 41 33 22 24 27 27 23 28 35 22 Construct a 95% confidence interval for the mean activation time for the sprinklers. An inference procedure is called _____________ if the probability calculations involved in that procedure remain fairly accurate when a condition for using the procedure is violated. SUMMARY/QUESTIONS TO ASK IN CLASS