Chapter 8: Estimating with Confidence
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1 Chapter 8: Estimating with Confidence Key Vocabulary: point estimator point estimate confidence interval margin of error interval confidence level random normal independent four step process level C confidence interval degrees of freedom standard error one -sample z interval t distribution t-procedures one-sample t interval robust 8.1 Confidence Intervals: The Basics (pp ) 1. A point estimator is a statistic that 2. The value of the point estimator statistic is called a and it is our "best guess" at the value of the. 3. Summarize the facts about sampling distributions learned in chapter 7: Shape Center Spread
2 4. In statistics, what is meant by a 95% confidence interval? 5. A confidence interval takes the form of : estimate margin of error where: estimate = margin of error = 6. Define a level C confidence interval. 7. What information does the margin of error provide? 8. Sketch and label a 95% confidence interval for the standard normal curve. 9. In a sampling distribution of x, why is the interval of numbers between x 2s called a 95% confidence interval? 10. Sketch and label a 90% confidence interval for the standard normal curve. 11. Interpret a Confidence level: "To say that we are 95% confident is shorthand for Explain how to interpret a Confidence interval. 13. Does the confidence level tell us the chance that a particular confidence interval captures the population parameter? If not, what does it tell us?
3 14. What does the critical value depend on? 15. Write the form for calculating a confidence interval as shown on page Why do we want high confidence and a small margin of error? 17. Explain the two conditions when the margin of error gets smaller. 18. State the three conditions for constructing a confidence interval for p or. Random Normal Independent 19. What are the two important reminders for constructing and interpreting confidence intervals?
4 8.2 Estimating a Population Proportion (pp ) 1. In statistics, what is meant by a sample proportion: ˆp? 2. Give the mean and standard deviation for the sampling distribution of ˆp? 3. How does the standard deviation differ to to standard error for the sampling distribution of ˆp? 4. Describe the sampling distribution of a sample proportion ˆp as learned in section 7.2. Shape Center Spread 5. Define standard error. 6. In general what is meant by the standard error of a statistic? 7. How do you calculate the standard error of ˆp? 8. What is the formula for a one-sample z interval for a population proportion? Describe how to construct a level C confidence interval for a population proportion.
5 9. Describe the four step process on how to contruct and interpret a confidence interval. State Plan Do Conclude 10. What formula is used to determine the sample size necessary for a given margin of error? 11. What conditions must be met in order to use z procedures for inference about a proportion? 12. What does z* represent? 13. What is the value of z* for a 95% confidence interval? Include a sketch. 14. What is the value of z* for a 90% confidence interval? Include a sketch. 15. What is the value of z* for a 99% confidence interval? Include a sketch.
6 8.3 Estimating a Population Mean (pp ) 1. What is the formula for a one-sample z interval for a population mean? Describe how to construct a level C confidence interval for a population mean. 2. What is the formula for the margin of error of the confidence interval for the population mean? 3. How can you arrange to have both high confidence and a small margin of error? 4. Describe the three steps for choosing a sample size for a desired margin of error when estimating. 5. What happens to the margin of error as z* gets smaller? Does this result in a higher or lower confidence level? 6. What happens to the margin of error, as gets smaller? 7. What happens to the margin of error, as n gets larger? By how many times must the sample size n increase in order to cut the margin of error in half? 8. The formula used to determine the sample size n that will yield a confidence interval for a population mean with a specified margin of error m is z * s ME. Solve for n. n
7 9. It is the size of the that determines the margin of error. The size of the does not influence the sample size we need. 10. Complete the Check Your Undertanding on page How do you calculate the degrees of freedom for a t distribution? 12. What happens to the t distribution as the degrees of freedom increase? 13. How would you construct a t distribution? 14. Describe the differences between a standard normal distribution and a t distribution. 15. Describe the similarities between a standard normal distribution and a t distribution. 16. What is the formula for the standard deviation of the sampling distribution of the sample mean x? 17. What is the standard error of the sample mean x? 19. Describe how to construct the one-sample t interval for a population mean?
8 20. Summarize the three conditions for inference about a population mean: Random Normal Independent 21. Inferences for proportions use and inferences for means use. 22. What does it mean if an inference procedure is robust? 23. If the size of the SRS is less than 15, when can we use t procedures on the data? 24. If the size of the SRS is at least 15, when can we use t procedures on the data? 25. If the size of the SRS is at least 30, when can we use t procedures on the data? 26. Summarize the details of the four step procedure for estimating p: State Plan Do Conclude
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9. Interpret a Confidence level: "To say that we are 95% confident is shorthand for..
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