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QMB 3200 – Homework #4 Instructions: 1) Solve all the problems. Each problem carries 10 points. Maximum score possible for this Homework is 100 points. 2) Presenting only the final answer is not sufficient to get complete credit. Show the steps in solution approach. That way partial credit can be earned to various steps in final solution. It is your responsibility to demonstrate mastery of the subject matter through your answers. 3) Submit your report as an Excel file. Solve each problem on a separate tab (worksheet). You must use Excel formulas and functions to solve the problems. Organize your solutions on the Excel worksheet properly. Show where your answers are for each problem and the sections of the problem. Use proper formatting. Name Your File to show your Full Name and the HW Number. Upload your report file on Canvas and verify if everything is fine by opening up the uploaded file. It is your responsibility to ensure your report is uploaded properly. 4) Do not wait until the last minute. The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted. If your file does not appear on Canvas by the deadline, zero points will be recorded for you for that HW. No exceptions are entertained for any reason under any circumstance in this regard. HW Problems: 1. Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per treatment of Herceptin, a drug used to treat breast cancer. Typical treatment costs (in dollars) for Herceptin are provided by a simple random sample of 10 patients. 5798 7446 5119 5376 5495 5237 4814 6578 3717 5920 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. 2. If I have a population which is normally distributed with a mean and std. dev. of 120 and 20 respectively, what is the mean and the standard deviation of the sampling distribution of the mean using a sample size of a. 16 b. 25 c. 36 d. 100 3. The average price of a gallon of unleaded regular gasoline was reported to be $3.44 in northern Kentucky. Use this price as the population mean and assume the population standard deviation is $0.30. a. What is the probability that the mean price for a sample of 50 service stations is within ±$.06 of the population mean? b. What is the probability that the mean price for a sample of 100 service stations is within ±$.06 of the population mean? 4. The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually. The average cost per person for crashes in the Tampa, Florida, area was reported to be $1900. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is known to be $500. What is the 90% confidence interval of the average cost per person for crashes in Tampa? What would you recommend if the study required a margin of error of $150 or less? 5. If I have a population of an unknown mean, what is the 95% confidence interval estimate of the population mean if a. A random sample of size 36 gives a mean of 50 and a standard deviation of 12. b. A random sample of size 49 gives a mean of 50 and a standard deviation of 12. c. Interpret the confidence intervals obtained in parts “a” and “b”. In other words, write an English sentence on what that those confidence intervals mean. 6. For the above problem (Problem #5), a. Find the 99% confidence interval estimates b. Find the 90% confidence interval estimates c. Interpret the confidence intervals obtained in parts a and b. In other words, write an English sentence on what that those confidence intervals mean. 7. If I have a population of an unknown mean and unknown standard deviation, what is the 95% confidence interval estimate of the mean if a. A random sample of size 25 gives a mean of 50 and a standard deviation of 12 b. A random sample of size 16 gives a mean of 50 and a standard deviation of 12 8. The average cost per night of a hotel room in New York City is $325. Assume this estimate is based on a sample of 100 hotels and that the sample standard deviation is $75. a. What is the 95% confidence interval estimate of the population mean? b. What is the 99% confidence interval estimate of the population mean? 9. The average cost per night of a hotel room in San Francisco is $550 with a standard deviation is $150 based on a sample of 50 hotel room rates. a. Clearly state what the random variable in this problem is? b. What is an appropriate distribution to be used for finding the confidence intervals for this problem and why? c. Construct a 99% confidence interval estimate on the mean of all hotel room rates. d. What is the 90% confidence interval estimate? e. What is the 95% confidence interval estimate? 10. If I have a sample of 200 randomly selected people in a city of whom 120 are Christians, what would be a 95% confidence interval for the proportion of Christians in that city? If I want my confidence interval with a margin of error of 1% or less, how many people should I have in my sample? (Note: This problem is similar to the solved example problem on page 8 of “Chapter04ConfidenceIntervals.docx”. Refer to the same before solving this problem in Excel using Excel formulas and functions).

 

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