# Statistics Chapter 8 - Confidence Intervals

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1. What is the status of for z-based confidence intervals for a population mean? is known
2. What is the status of for t-based confidence intervals for population mean? is unknown
3. What two things does Statistical Inference involve?
• Estimation
• Hypothesis
4. What do we use statistical inferences for?
To make inferences about a parameter
5. What are the two types of estimates of parameters?
• Point estimate
• Interval estimate
6. What is a Interval Estimate?
It's a point estimate with a +/- Margin of Error
7. What is the purpose of an Interval Estimate?
Provide info about how close the point estimate is to the parameter
8. In an Interval Estimate, what does the Width depend on?
How much confidence you want in your estimate
9. What is Precision?
Width of an interval
10. What is Accuracy?
Probability of the estimate being correct, defined as 11. What is the general form of the interval estimate for the population mean? +/- Margin of Error
12. What is the interval estimate of equation if is known? 13. What is ?
The confidence coefficient
14. What is ?
The z-value that provides an area of in the upper tail of the standard normal prob distribution
15. Assume:
Population of all individual car mileages is ND
Standard deviation ( ) is 0.8
A sample size (n) of 50
Build a 95% interval estimate of • We have 95% confidence that will be within +/- .22 mpg of the population mean
• • (from z-table)
• Margin of error = (1.96)(.113) = .22
16. If we have 95% confidence that will be within +/- .22 mpg of the population mean...
Assume = 31.56
What is the confidence interval?
[31.56 +/- 0.22] = [31.34, 31.78]
17. If = 0.10 (90% confidence) what is the confidence interval width?
1.645
18. If = 0.05 (95% confidence) what is the confidence interval width?
1.96
19. If = 0.01 (99% confidence) what is the confidence interval width?
2.576
20. What probability of values is between z-scores of -1.645 and +1.645?
0.9000
21. What probability of values is between z-scores of -1.96 and +1.96?
0.9500
22. What probability of values is between z-scores of -2.576 and +2.576?
0.9900
23. What is used instead of when it is not known?
• s
• Sample standard deviation
24. What is the t-score standard error equation? 25. What is the t-score equation? 26. What are the differences between the t-distribution and the z-distribution?
• t-distribution is more spread out than the standard normal (z-distribution)
• t-distribution is defined by the # of degrees of freedom (df = n - 1)
27. What happens to the degrees of freedom (df) as n (sample size) increases?
df increases
28. What happens to the t-curve as the degrees of freedom (df) increases?
• t-curve narrows
• Eventually approaches the standard normal curve
29. At what sample size does the t-curve become very similar to the z-curve? 30. At what sample size is the z-distribution used INSTEAD of the t-distribution? 31. What's the differences between the t-table and the z-table?
• t-table shows values to the RIGHT of the t-score
• t-table is based on df and not n
32. What is the Confidence Interval equation for the t-distribution ( is not known)? 33. In a sample of 16 management consultants, the following statistics about hourly wages have been computed:  Construct a  95% confidence interval (C.I.) estimate. • • • • Author: honestkyle ID: 211890 Card Set: Statistics Chapter 8 - Confidence Intervals Updated: 2013-04-11 18:51:02 Tags: confidence intervals probability stats Folders: Description: Confidence Intervals Show Answers: