. What can you do to ensure that
?
1. (a) You are an experimenter about to take n measurements
. What can you do to ensure that
?
(b) You are a statistician and an experimenter has given you
n numbers 
. What are all
the things you can do to test the assumption that 
?
(c) Write out the statement 
in matrix form.
2. Let 
and define
. Find 
and hence find 
. Compare 
to 
, where 
.
3. A firm manufactures training weights. Because of variations in
the casting process, the actual weight of a "10-kg" weight will vary
according to a 
distribution.
To be accepted, a weight must be within 100 g of the target
weight.
(a) What is the probability that a given weight will be outside the acceptance limits?
(b) If 10 randomly-selected weights are tested, what is the probability that all of them will be within the acceptance limits?
(c) Could you use the normal approximation to the binomial to
compute the answer to (b)? Explain.
4. Suppose you measured a temperature 10 times and found a mean of 78.56º C and a standard deviation of 2.05º C. Give a 95% confidence interval for the true mean temperature, stating any assumptions you make.