All material presented in the Estimation Chapter 1. When would the mean

All material presented in the Estimation Chapter
1. When would the mean grade in a class on a final exam be considered a statistic?
When would it be considered a parameter?
2. Define bias in terms of expected value.
3. Is it possible for a statistic to be unbiased yet very imprecise? How about being very accurate but biased?
4. Why is a 99% confidence interval wider than a 95% confidence interval?
5. When you construct a 95% confidence interval, what are you 95% confident about?
6. What is the difference in the computation of a confidence interval between cases in which you know the population standard deviation and cases in which you have to estimate it?
7. Assume a researcher found that the correlation between a test he or she developed and job performance was 0.55 in a study of 28 employees. If correlations under .35 are considered unacceptable, would you have any reservations about using this test to screen job applicants?
8. What is the effect of sample size on the width of a confidence interval?
9. How does the t distribution compare with the normal distribution? How does this difference affect the size of confidence intervals constructed using z relative to those constructed using t? Does sample size make a difference?
10. The effectiveness of a blood-pressure drug is being investigated. How might an experimenter demonstrate that, on average, the reduction in systolic blood pressure is 20 or more?
11. A population is known to be normally distributed with a standard deviation of 2.8. (a) Compute the 95% confidence interval on the mean based on the following sample of nine: 8, 9, 10, 13, 14, 16, 17, 20, 21. (b) Now compute the 99% confidence interval using the same data.
12. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What
conclusion can you draw about this test of his ability to predict the future?
13. What does it mean that the variance (computed by dividing by N) is a biased statistic?
14. A confidence interval for the population mean computed from an N of 16 ranges from 12 to 28. A new sample of 36 observations is going to be taken.
You can’t know in advance exactly what the confidence interval will be
because it depends on the random sample. Even so, you should have some idea of what it will be. Give your best estimation.
15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the standard deviation of the population is 10.
What is the 99% confidence interval on the population mean? (b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?