Hints on Review Problems for Second Exam (M 358K, Sp 06 Smith)
2.
g. How many samples do you have?
k. See p. 142 of the textbook.
m. Do you have two independent samples?
3. What famous theorem applies? And how does it answer the question?
6. i. There's a misprint: The first sentence in quotes should read, "95% of the time ...," instead of "90% of the time ... ".
ii. Think about the confidence interval demo and the diaram on p. 386.
iii. Does the confidence interval
depend on the sample chosen? Does the population mean depend on the
sample chosen?
iv. The definition on p. 386 is not precise enough for this class:
Remember that the "probability" in the book definition refers to the
probability space of all simple random samples of the same size as the sample we are using.
8. Try this: Let X be the weight of a (randomly chosen) medium orange. Let Y be the
weight of a (randomly chosen) large orange. We want to find P(X >
Y). This is the same as P(X - Y > 0). So you need to figure out what
the distribution of X - Y is.
9. How do the standard deviations of the three distributions compare?
11. See hints for #6.
13. The definition of p-value on p. 405 of the book is not precise
enough for this class: Remember that in defining the p-value, we are
only considering test statistics for simple random samples of the same size.