## COMM 291 Application of Statistics in Business (fall 2015)

COMM 291Application of Statistics in Business (fall 2015)ASSIGNMENT 5Hard Copy Solutions to be Handed In2:30 pm, Wednesday November 18, 2015Instructions:This assignment consists of 10 questions/problems. Answer/solve the questions/problems in the sameorder they are asked.Use the posted cover page. This is mandatory. Assignments without properly completed cover pageswill be penalised by reducing one mark.When formatting numbers in Excel, display only as many decimal places as provide decision-makingvalue to the reader. Similarly, any computations made by hand should be rounded to as many decimalplaces (and no more) as required by the reader to make an informed decision. Maintain all precision inyour calculations when performing multi-step computations and round only final reported figures.Problem 1 (4 points)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 thismorning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 tobe defective.a. What is the estimated proportion that was defective in the population? (1 point)b. Develop a 95% confidence interval for the proportion that was defective. (2 points)c. Zack has an agreement with his supplier that he is to return lots that are 10% or more defective.Should he return this lot? Explain your decision. (1 point)Problem 2 (4 points)Suppose that the prime minister wants an estimate of the proportion of the population that supports hiscurrent policy on health care. The prime minister wants the estimate to be within 0.04 of the trueproportion. Assume a 95% level of confidence. The prime minister’s political advisors estimated theproportion supporting the current policy to be 0.60.a. How large a sample is required? (2 points)b. How large a sample would be necessary if no estimate were available for the proportion thatsupports current policy? (2 points)Problem 3 (4 points)The manager of Apache Burger felt that an average of 70 customers made purchases daily between thehours of 3 p.m. and 5 p.m. A random sample over 50 days showed the sample mean to be 68.6 customerswith a standard deviation of 8.2 hours.a. Using the sample data, construct a 99% confidence interval for the population mean. (2 points)b. Does the 99% confidence interval include the value suggested by the manager? Interpret thisresult. (1 point)c. Suppose you decided to switch from a 99% confidence interval to a 95% confidence interval.Without performing any calculations, will the interval increase, decrease, or stay the same?Which of the values in the formula will change? (1 point)Problem 4 (4 points)The Simcoe County Food Emporium claims that âthe typical customer spends $60 per visit.â A sample of12 customers revealed the following purchases, in dollars, spent last visit:646664665962676164585466a. What is the point estimate of the population mean and standard deviation? (1 point)b. Develop a 90% confidence interval for the population mean. (2 points)c. Is the restaurant’s claim that the âtypical customerâ spends $60 per visit reasonable? Justify youranswer. (1 point)Problem 5 (6 points)The National Bank, like most other large banks, found that using automatic teller machines (ATMs)reduces the cost of routine bank transactions. National installed an ATM in the corporate offices of theFun Toy Company. The ATM is for the exclusive use of Fun’s 605 employees. After several months ofoperation, a sample of 100 employees revealed the following use of the ATM machine by Fun employeesin a month:# of time ATM used012345Frequency25302010105a. What is the estimate of the proportion of employees who do not use the ATM in a month? (1point)b. Develop a 95% confidence interval for this estimate. Can National be sure that at least 40% of theemployees of Fun Toy Company will use the ATM? (2 points)c. How many transactions does the average Fun employee make per month? (1 point)d. Develop a 95% confidence interval for the mean number of transactions per month. (1 point)e. Is it possible that the population mean is 0? Explain. (1 point)Problem 6 (3 points)A research organization surveyed 1016 Canadian adults (assume 50/50 split between men and women)and found that 65% of men and 45% of women support scrapping the penny.a. Construct a 90% confidence interval for the difference in support for scrapping the pennybetween men and women. (1 point)b. Construct a 99% confidence interval for the difference in support for scrapping the pennybetween men and women. (1 point)c. Interpret the meaning of the fact that one of these confidence intervals is wider than the others. (1point)Problem 7 (5 points)The owner of Britten’s Egg Farm wants to estimate the mean number of eggs laid per chicken. A sampleof 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs permonth.a. What is the value of the population mean? What is the best estimate of this value? (1 point)b. Explain why we need to use the t distribution. What assumption do you need to make? (1 point)c. For a 95% confidence interval, what is the value of t? (1 point)d. Develop the 95% confidence interval for the population mean. (1 point)e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs? (1point)Problem 8 (5 points)Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives ofInternet companies. She has developed a questionnaire that she believes measures stress. A score above80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stresslevel scores:9478839078999790979093941007584a. Find the mean stress level for this sample. What is the point estimate of the population mean? (1point)b. Construct a 95% confidence level for the population mean. (1 point)c. Is it reasonable to conclude that Internet executives have a mean stress level in the dangerouslevel, according to Dr. Benner’s test? (1 point)Problem 9 (6 points)The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can bedriven before the tread wears out is 96 600 km. The population standard deviation of the mileage is 8050km. The Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 95 795km. Is Crosset’s experience different from that claimed by the manufacturer at the 0.05 level ofsignificance.a.b.c.d.e.What are the hypotheses? Is this a one- or two-tailed test? (1 point)What is the decision rule? (1 point)What is the value of the test statistic? (1 point)What is your decision regarding H0? (1 point)Determine the p-value and interpret it. (2 points)Problem 10 (4 points)During the recent seasons, Major League Baseball has been criticized for the length of games. A reportindicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed thefollowing times to completion. (Note that the minutes have been changed to fractions of hours, so that agame that lasted 2 hours and 24 minutes is reported at 2.40 hours.)Can we conclude that the mean time for a game is less than 3.50 hours? Use the 0.05 significance level.

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