Problem 1
When would the mean grade in a class on a final exam be considered a statistic? When would it be considered a parameter?
Problem 2
Define bias in terms of expected value.
Problem 3
Is it possible for a statistic to be unbiased yet very imprecise? How about being very accurate but biased?
Problem 4
Why is a \(99 \%\) confidence interval wider than a \(95 \%\) confidence interval?
Problem 5
When you construct a \(95 \%\) confidence interval, what are you \(95 \%\) confident about?
Problem 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?
Problem 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?
Problem 8
What is the effect of sample size on the width of a confidence interval?
Problem 9
How does the t distribution compare with the normal distribution? How does this difference affect the size of confidence intervals constructed using \(\mathrm{z}\) relative to those constructed using t? Does sample size make a difference?
Problem 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?
