Homework 4 : Questions( from the 11th edition of the book)
Chapter 7: 15,43,45,52
Question 15:
Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per
treatment of Herceptin, a drug used to treat breast cancer (BusinessWeek, Jan 30, 2006).
Typical Treatment costs ( In Dollars ) for Herceptin, are provided by simple random sample of
10 patients.
4376
4798
5578
6446
2717
4119
4920
4237
4495
3814
A) Develop a point estimate of the mean cost per treatment with Herceptin.
B) Develop a point estimate of the standard deviation of the cost per treatment with Herceptin.
Question 43:
Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the
average annual medical spending per enrollee was $3267; in 2003, the average annual
Medicare spending per enrollee was $6883 (Money, Fall 2003). Suppose you hired a consulting
firm to take a sample of fifty 2003 Medicare enrollee to further investigate the nature of
expenditures. Assume the population standard deviation for 2003 was $2000.
A) Show the sampling distribution of the mean amount of Medicare spending for a sample of
fifty 2003 enrollees.
B) What is the probability the sample mean will be within +/- $300 of the population mean?
C) What is the probability the sample mean will be greater than $7500? If the consulting firms
tells you the sample mean for the Medicare enrollees they interviewed was $7500, would
you question whether they followed correct simple random sampling procedures ? Why or
why not?
Question 45:
The mean television viewing time for Americans is 15 hours per week( Monday, November
2003). Suppose a sample of 60 Americans is taken to further investigate viewing habits.
Assume the population standard deviation for weekly viewing time is σ = 4 Hours.
A) What is the probability that the sample mean will be within 1 hour of the population mean?
B) What is the probability the sample mean will be within 45 min of the population mean?
Question 52:
Advertisers contract with internet service providers and search engines to place ads on
websites. They pay a fee based on the number of potential customers who click on their ad.
Unfortunately, click fraud- The practice of someone clicking on an ad solely for the purpose of
driving up advertising revenue- has become a problem. Forty percent of advertisers claim they
have been a victim of click fraud( BusinessWeek, March 12, 2006). Suppose a simple random
sample of 380 advertisers will be taken to learn more abut how they are affected by this
practice.
A) What is the probability that the sample proportion will be within +/- 0.04 of the population
proportion experiencing click fraud?
B) What is the probability that the sample proportion will be greater then 0.45?
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Homework 4
Chapter 8: 3,16,28,38
Question 3:
A simple random sample of 60 items resulted in a sample mean of 80.
The population standard deviation is σ = 15.
Compute 95% confidence interval for the population mean.
A) Assume that the same sample mean was obtained from a sample of 120 items. Provide a
95% confidence interval for the population mean.
B) What is the effect of a larger sample size on the interval estimate.
Question 16:
The mean number of hours of flying time for pilots at continental airlines is 49 hours per month.
Assume that this mean was based on actual flying times for a sample of 100 continental airlines
pilots and that the sample standard deviation was 8.5 hours.
A) At 95% Confidence, what is the margin of error?
B) What is the 95% Confidence Interval estimate of the population mean flying time for the
pilots?
C) The mean number of hours of hours of flying time for pilots at United Airlines is 36 hours per
month. Use your results from Part B to discuss differences between the flying times for the
pilots at the two airlines. The Wall Street journal reported United Airlines as having highest
labor cost among all airlines. Does the information in this exercise provide insight as to why
united Airlines might expect higher labor costs?
Question 28:
An Online survey by ShareBuilder, a retirement plan provider, and Harris Interactive reported
that 60% of female business owners are not confident they are saving enough for retirement(
SmallBiz, Winter 2006). Suppose we would like to do a follow-up study to determine how much
female business owners are saving each year toward retirement and want to use $100 as the
desired margin of error for an interval estimate of the population mean. Use $1100 as a
planning value for the standard deviation and recommend a sample size for each of the
following situations.
A) A 90% Confidence Interval is desired for the mean amount saved.
B) A 95% Confidence Interval is desired for the mean amount saved.
C) A 99% Confidence Interval is desired for the mean amount saved.
D) When the desired margin of error is set, what happens to the sample size as the confidence
interval is increased? Would you recommend using a 99% confidence interval in this case?
Discuss.
Question 38:
According to Thomson Financial, through January 25, 2006, the majority of companies reporting
profits had beaten estimates ( BusinessWeek, February 6,2006). A sample of 162 companies
showed 104 beat estimates, 29 matches estimates and 29 fell short.
A) What is the point estimate of the proportion that fell short of estimates
B) Determine the margin of error and provide a 95% Confidence Interval for the proportion that
beats estimates
C) How large a sample is needed if the desired margin of error is 0.05?