## Statistics Problems & Answers

**Statistics Problems & Answers****A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a population standard deviation of $ 5. A sample of 49 steady smokers revealed that . a. What is the point estimate of the population mean? Explain what it indicates. b. Using the 95 percent level of confidence, determine the confidence interval for . Ex-plain what it indicates.**

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**Refer to the previous exercise. Suppose that 64 smokers (instead of 49) were sampled. Assume the sample mean remained the same. a. What is the 95 percent confidence interval estimate of ? b. Explain why this confidence interval is narrower than the one determined in the previous exercise.**

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**Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation 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 point estimate of the population mean? b. Develop a 99 percent confidence interval for the population mean. c. Interpret the meaning of part ( b).**

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**Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10 A. M. section of 40 students, the mean number of misspelled words was 6.05. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.**

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**The owner of Britten’s Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month. a. What is the value of the population mean? What is the best estimate of this value? b. Explain why we need to use the t distribution. What assumption do you need to make? c. For a 95 percent confidence interval, what is the value of t? d. Develop the 95 percent confidence interval for the population mean. e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs?**

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**Merrill Lynch Securities and Health Care Retirement Inc. are two large employers in down-town Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of the feasibility study, they wish to estimate the mean weekly child- care cost of their employees. A sample of 10 employees who use child care reveals the following amounts spent last week. $ 107 $ 92 $ 97 $ 95 $ 105 $ 101 $ 91 $ 99 $ 95 $ 104 Develop a 90 percent confidence interval for the population mean. Interpret the result.**

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**The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling. 29 38 38 33 38 21 45 34 40 37 37 42 30 29 35**

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**Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election. a. Estimate the value of the population proportion. b. Develop a 99 percent confidence interval for the population proportion. c. Interpret your findings.**

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**The Fox TV network is considering replacing one of its prime- time crime investigation shows with a new family- oriented comedy show. Before a final decision is made, net-work executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show. a. Estimate the value of the population proportion. b. Develop a 99 percent confidence interval for the population proportion. c. Interpret your findings.**

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**Schadek Silkscreen Printing Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective. a. What is the estimated proportion defective in the population? b. Develop a 95 percent confidence interval for the proportion defective. c. Zack has an agreement with his supplier that he is to return lots that are 10 percent or more defective. Should he return this lot? Explain your decision.**