1.An economist uses the price of a gallon of milk as a measure of inflation. She finds that
the average price is $3.50 per gallon and the population standard deviation is $0.33. You
decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute
the mean price for the sample.
a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between $3.46 and $3.54?
c. What is the probability that the difference between the sample mean and the population
mean is less than $0.01?
d. What is the likelihood the sample mean is greater than $3.60?
2. Refer to the Buena School District bus data. Information provided by manufacturers of
school buses suggests the mean maintenance cost per month is $455 per bus. Use statistical
software to find the mean and the standard deviation for the Buena buses. Does the
Buena data seem to be in line with that reported by the manufacturer? Specifically, what is
the probability of the sample mean being less than Buena’s, given the manufacturer’s data?
3. Families USA, a monthly magazine that discusses issues related to health and health costs,
surveyed 20 of its subscribers. It found that the annual health insurance premiums for a
family with coverage through an employer averaged $10,979. The standard deviation of the
sample was $1,000.
a. Based on this sample information, develop a 90% confidence interval for the population
mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99%
4. Near the time of an election, a cable news service performs an opinion poll of 1,000 probable
voters. It shows that the Republican contender has an advantage of 52% to 48%.
a. Develop a 95% confidence interval for the proportion favoring the Republican
b. Estimate the probability that the Democratic candidate is actually leading.
c. Repeat the above analysis based on a sample of 3,000 probable voters.
5. Refer to the Buena School District bus data.
a. Develop a 95% confidence interval for the mean bus maintenance.
b. Develop a 95% confidence interval for the mean bus miles.
c. Write a business memo to the state transportation official to report your results.
Case study: Century National Bank
Refer to the description of Century National Bank at the end
of the Review of Chapters 1–4 on page 125. When Mr. Selig
took over as president of Century several years ago, the use
of debit cards was just beginning. He would like an update
on the use of these cards. Develop a 95% confidence interval
for the proportion of customers using these cards. On
the basis of the confidence interval, is it reasonable to conclude
that more than half of the customers use a debit
card? Write a brief report interpreting the results.
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