Download Unit 6 - UCSB C.L.A.S.

PSTAT 5A
Unit 6 Practice Problems
1. A researcher is interested in the mean price of all airfare prices (in dollars)
for a one-way ticket from Atlanta to Chicago. In a random sample of 35
airfare prices, the average was found to be $101.78 with a standard
deviation of $6.70.
A. Define the parameter and random variable of interest.
B. What is the distribution of the sample mean?
C. Construct a 95% CI for the mean price. Interpret this CI.
D. If σ = $11, construct the 95% CI for the mean price.
E. Suppose that all airfare prices follow a normal distribution with σ =
$11. How many fares must be included in your sample if you want to
be 95% confident that the sample mean is within $2 of the population
mean?
2. A box of oatmeal is listed as containing 10 ounces. A shopper is worried that
the company is systematically under-filling the boxes. He found that a
random sample of 76 boxes had an average weight of 9.876 ounces with a
sample standard deviation of 0.483.
A. Define the parameter and random variable of interest.
B. Identify the appropriate distribution for this type of study.
C. State the null and alternative hypotheses for this test.
D. Calculate the test statistic.
E. Calculate the p-value.
F. State your decision and report your conclusion at the 1% level of
significance.
3. A toy company claims that its glow sticks will last an average of 13 minutes.
Timmy purchases 5 such glow sticks and finds the average lifetime of the
glow sticks to be 13.23 minutes. Assume that the lifetimes of these glow
sticks follow a normal distribution with a standard deviation of 0.5 minutes.
Test the company’s claim at a 5% level of significance.