STM: p. 314: 1,2,4-6
p. 322, 1,2,4
p. 579: 5
p. 589: 1, 2,4,6,8,
p. 736: 10,11 (Note: "standard error" is defined as the SD of Xbar
-- that is the standard deviation of the average.)
p. 334: 2,4ab (skip c)
p. 342: 1,4
p. 353: 1,2,6
Consider the classdata
again. Suppose that, for some reason, I needed to know what a typical
commuting time was for students in this class. But for some reason
I didn't have time to ask everyone in the class, again, and so instead
I selected a random sample of 5 students WITH REPLACEMENT and asked them.
a) What's the population and what's the sample?
b) Find the SD and mean of the population.
c) Using Data Desk, select a random sample of size 5 and calculate
the average. If you used this as the estimate of the population mean,
what would your estimate be and how far off would it be?
d) Now take 100 samples of size 5 (with replacement), and for each
sample calculate the average. What's the SD of this sample of averages?
e) The theoretical standard error is the SD of the population divided
by square-root of the sample size. What is this value, and how does
it compare to your answer in (d)?
f) Make a histogram of the population and of your 100 averages.
Are the shapes similar? Describe the shape of the averages.
g) Repeat c-f using sample sizes of 25.