An economist uses the price of a gallon of milk as a measure of inflation. She finds that

Dated: 15th May'18 08:18 PM
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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

b. How large a sample is needed to find the population mean within \$250 at 99%

confidence?

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

candidate.

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.

An economist uses the price of a gallon of milk as a measure of inflation. She finds that
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