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ELF-REVIEW 9-1 The Bun and Run is a franchise fast-food restaurant located in the Northeast specializing in hall pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French es also are available. The Marketing Department of Bun-and-Run Inc. reports that the distributlon of daily sales for their restaurants follows the normai distritbution and that the population standard deviation is $3,000. A sample of 40 franchises showed the mean daily sales to be $20,000. (a) What is the populetion mean of dally sales for Bun-and Run franchises? (b) What is the best estimate of the population mean? What is this value called? () Develop a 95% confidence interval for the popuiation mean of daily sales (d) Interpret the confidence Intervel,

ELF-REVIEW 9-1 The Bun and Run is a franchise fast-food restaurant located in the Northeast specializing in hall pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French es also are available. The Marketing Department of Bun-and-Run Inc. reports that the distributlon of daily sales for their restaurants follows the normai distritbution and that the population standard deviation is $3,000. A sample of 40 franchises showed the mean daily sales to be $20,000. (a) What is the populetion mean of dally sales for Bun-and Run franchises? (b) What is the best estimate of the population mean? What is this value called? () Develop a 95% confidence interval for the popuiation mean of daily sales (d) Interpret the confidence Intervel,

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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rOr or the possibility that a particular random sample may not be a good repre- entation of the population. In each of these four samples, the mean of the sample either much less or much more than the population mean. Because of random sampling, the mean of the sample is not a good estimate of the population mean, nd the confidence Interval based on the sample's mean does not include the pop- ulation mean. ELF-REVIEW 9-1 The Bun-and-Run is a franchise fast-food restaurant located in the Northeast specializing in half-pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French es also are available. The Marketing Department of Bun-and-Run Inc. reports that the distributlon of daily sales for their restaurants follows the normal distribution and that the population standard deviation Is $3,000. A sample of 40 franchises showed the mean daily sales to be $20,000. (a) What is the population mean of dally sales for Bun-and-Run franchises? (b) What Is the best estimate of the population mean? What is this value called? ic) Develop a 95% confidence interval for the popuiation mean of daily sales. (d) Interpret the confidence interval, EXERCISES 1. A sample of 49 observations Is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99 % confidence Interval for the population mean. 2. A sample of 81 observations Is taken from a normal population with a standard deviation of 5. The sample mean Is 40. Determine the 95% confidence Interval for the population mean. bnal 3. A sample of 250 observations Is selected from a normal population with a popula- tlon standard devlation of 25. The sample mean Is 20. a. Determine the standard error of the mean. b. Explain why we can use formula (9-1) to determlne the 95% confidence interval. c. Determine the 95% confidence Interval for the population mean. 4. Suppose you know a and you want an 85% confidence level. What value would you use as z in formula (9-1)7 5. A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week. They found the distribution of weekly spending followed the normal distributlon with a population standard devlation of $5. A sam- pie of 49 Americans revealed that $20. a. What is the point estimate of the population mean? Explain what It Indicates. b. Using the 95% level of confidence, determine the confidence Interval for p. Ex- plain what it indicates. 6. Refer to the prevlous exercise. Instead of 49, suppose that 64 Americans were sur- veyed about their weekly expenditures on coffee. Assume the sample mean re- mained the same. a. What is the 95% confidence Interval estimate of u? h. Explaln why this confidence Interval is narrower than the one determined In the prevlous exercise. 7. Bob Nale is the owner of Nale's Quick Fill. Bob would lke to estimate the meen number of gallons of gasollne sold to his customers. Assume the number of gallons sold follows the normal distributlon with a population standard devlation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold Is 8.60. a. What is the polnt estimate of the population mean? b. Develop a 99% confidence Interval for the population mean. c. Interpret the meaning of part (b). CHE
Transcribed Image Text:rOr or the possibility that a particular random sample may not be a good repre- entation of the population. In each of these four samples, the mean of the sample either much less or much more than the population mean. Because of random sampling, the mean of the sample is not a good estimate of the population mean, nd the confidence Interval based on the sample's mean does not include the pop- ulation mean. ELF-REVIEW 9-1 The Bun-and-Run is a franchise fast-food restaurant located in the Northeast specializing in half-pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French es also are available. The Marketing Department of Bun-and-Run Inc. reports that the distributlon of daily sales for their restaurants follows the normal distribution and that the population standard deviation Is $3,000. A sample of 40 franchises showed the mean daily sales to be $20,000. (a) What is the population mean of dally sales for Bun-and-Run franchises? (b) What Is the best estimate of the population mean? What is this value called? ic) Develop a 95% confidence interval for the popuiation mean of daily sales. (d) Interpret the confidence interval, EXERCISES 1. A sample of 49 observations Is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99 % confidence Interval for the population mean. 2. A sample of 81 observations Is taken from a normal population with a standard deviation of 5. The sample mean Is 40. Determine the 95% confidence Interval for the population mean. bnal 3. A sample of 250 observations Is selected from a normal population with a popula- tlon standard devlation of 25. The sample mean Is 20. a. Determine the standard error of the mean. b. Explain why we can use formula (9-1) to determlne the 95% confidence interval. c. Determine the 95% confidence Interval for the population mean. 4. Suppose you know a and you want an 85% confidence level. What value would you use as z in formula (9-1)7 5. A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week. They found the distribution of weekly spending followed the normal distributlon with a population standard devlation of $5. A sam- pie of 49 Americans revealed that $20. a. What is the point estimate of the population mean? Explain what It Indicates. b. Using the 95% level of confidence, determine the confidence Interval for p. Ex- plain what it indicates. 6. Refer to the prevlous exercise. Instead of 49, suppose that 64 Americans were sur- veyed about their weekly expenditures on coffee. Assume the sample mean re- mained the same. a. What is the 95% confidence Interval estimate of u? h. Explaln why this confidence Interval is narrower than the one determined In the prevlous exercise. 7. Bob Nale is the owner of Nale's Quick Fill. Bob would lke to estimate the meen number of gallons of gasollne sold to his customers. Assume the number of gallons sold follows the normal distributlon with a population standard devlation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold Is 8.60. a. What is the polnt estimate of the population mean? b. Develop a 99% confidence Interval for the population mean. c. Interpret the meaning of part (b). CHE
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