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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+c) Do you think the distribution of your driving times is unimodal and symmetric?
=+b) How often will it take you more than 24 minutes?
=+a) How often will you arrive at work in less than 22 minutes?
=+3 Suppose it takes you 20 minutes, on average, to drive to work, with a standard deviation of 2 minutes. Suppose a Normal model is appropriate for the distributions of driving times.
=+2 As a group, the Dutch are among the tallest people in the world. The average Dutch man is 184 cm tall—just over 6 feet (and the average Dutch woman is 170.8 cm tall—just over 5′7″). If a Normal model is appropriate and the standard deviation for men is about 8 cm, what percentage of all
=+The company president vetoes that plan, saying the company should give away less free cereal, not more. Her goal is to set the machine no higher than 16.2 oz and still have only 4% underweight boxes. The only way to accomplish this is to reduce the standard deviation. What standard deviation must
=+Suppose an MBA program says it admits only people with GMAT scores among the top 10%. How high a GMAT score does it take to be eligible?
=+what proportion of GMAT scores falls between 450 and 600?
=+Assuming the GMAT scores are nearly Normal with N(500,100),
=+Suppose you earned a 600 on your GMAT test. From that information and the 68–95–99.7 Rule, where do you stand among all students who took the GMAT?
=+b) Does this seem “fair”?
=+a) Which one will be dropped?
=+a standard deviation of 4 and the mean on the second was 75 with a standard deviation of 5,
=+1 Your Accounting teacher has announced that the lower of your two tests will be dropped. You got a 90 on test 1 and an 80 on test 2. You’re all set to drop the 80 until she announces that she grades “on a curve.” She standardized the scores in order to decide which is the lower one. If the
=+Use the 68–95–99.7 Rule to characterize how extraordinary the change on August 8, 2011 was. Is the rule appropriate?
=+c) The data are the mean driving distance for each golfer. Is that another concern in interpreting the interval?
=+b) Interpreting this interval raises some problems. Discuss.
=+a) Find a 95% confidence interval for the mean drive distance.
=+54. Driving distance 2013. How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.)Here’s a histogram of the average driving distances of the 190 leading professional golfers by May 5, 2013,
=+c) A diet guide claims that you will get an average of 120 calories from a serving of vanilla yogurt. What does this evidence indicate? Use your confidence interval to test an appropriate hypothesis and state your conclusion.
=+b) Create a 95% confidence interval for the average calorie content of vanilla yogurt.
=+53. Yogurt. Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:130 160 150 120 120 110 170 160 110 130 90
=+) State an appropriate conclusion.
=+d) Explain what the P-value means in this context.
=+c) Test the hypothesis and find the P-value.
=+b) Are the necessary assumptions to perform inference satisfied?
=+52. Fuel economy. A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg
=+e) What’s your conclusion?
=+d) Explain (in context) what this P-value means.
=+c) The online shoppers in our sample had an average age of 24.2 years, with a standard deviation of 5.3 years. What’s the P-value for this result?
=+b) We plan to test the null hypothesis by selecting a random sample of 40 individuals who have made an online purchase this year. Do you think the necessary assumptions for inference are satisfied? Explain.
=+) Write appropriate hypotheses.
=+51. E-commerce, part 2. The average age of online consumers a few years ago was 23.3 years. As older individuals gain confidence with the Internet, it is believed that the average age has increased. We would like to test this belief.
=+50. Performance standards. The U.S. Golf Association(USGA) sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and
=+49. E-commerce. A market researcher at a major clothing company that has traditionally relied on catalog mail-order sales decides to investigate whether the amount of monthly online sales has changed. She compares the mean monthly online sales of the past several months with a historical figure
=+a) Discuss the assumptions and conditions for using tmethods for inference with these data. Here are some plots that may help you decide what to do.150 100 50 Number of Houses 0Current Asking Price 0 $200,000 $400,000 $600,000 $800,000b) What would you report to the real estate agency about the
=+Exercises 393 to be $178,613.50 with a standard deviation of $92,701.56.You have been retained by the real estate agency to report on the current situation.
=+48. Real estate crash? After the sub-prime crisis of late 2007, real estate prices fell almost everywhere in the U.S.In 2006–2007 before the crisis, the average selling price of homes in a region in upstate New York was $191,300. A real estate agency wants to know how much the prices have
=+b) What would you tell the landowner about whether this site is suitable for a small wind turbine? Explain
=+47. Wind power. Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per hour, according to the Wind Energy Association. One
=+b) Based on your answer to parta, do you think that the audit times have, in fact, increased?
=+Find a 90% confidence interval estimate for the mean audit time.
=+a) Assume the conditions necessary for inference are met.
=+46. Tax audits, part 2. While reviewing the sample of audit fees, a senior accountant for the firm notes that the fee charged by the firm’s accountants depends on the complexity of the return. A comparison of actual charges therefore might not provide the information needed to set next
=+b) Based on your confidence interval, what do you think of the claim that the mean cost has changed?
=+a) Develop a 95% confidence interval estimate for the mean audit cost.
=+to ask the firm for assistance during the audit. A large accounting firm is trying to determine what fee to charge for next year’s returns. In previous years, the actual mean cost to the firm for attending a client audit session was $650.To determine if this cost has changed, the firm randomly
=+45. Tax audits. Certified public accountants are often required to appear with clients if the IRS audits the client’s tax return. Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advice and support from the accountant if the
=+) Suppose the standard deviation for the error in the measured speeds equals 4 mph. At 95% confidence, what sample size should be taken to ensure that the margin of error is no larger than {1.0 mph?
=+a) Discuss how the researchers may obtain a reasonable estimate of the standard deviation of error in the measured speeds.
=+44. Traffic speed, part 2. The speed-measuring machines must measure accurately to maximize effectiveness in slowing traffic. The accuracy of the machines will be tested before placement on city streets. To ensure that error rates are estimated accurately, the researchers want to take a large
=+b) The researchers commented that the interval was too wide. Explain specifically what should be done to reduce the margin of error to no more than {2 mph.
=+a) What is the margin of error for this problem?
=+43. Traffic speed. Police departments often try to control traffic speed by placing speed-measuring machines on roads that tell motorists how fast they are driving. Traffic M11_SHAR8696_03_SE_C11.indd 391 14/07/14 7:31 AM 392 CHAPTER 11 Confidence Intervals and Hypothesis Tests for Means safety
=+Casinos will use the information reported in the survey to estimate slot machine expenditure per hotel room. Do you think the estimates produced by the survey will accurately represent expenditures? Explain using the statistics reported and graph shown.
=+A recent survey of 500 visitors asked how much they spent on gambling. The average expenditure per room was $180.90 120 150 180 210 240 270 80 70 60 50 40 30 20 10 0Expenditures on Slot Machines (per hotel room)Number of Rooms
=+42. Convention revenues. At one time, Nevada was the only U.S. state that allowed gambling. Although gambling continues to be one of the major industries in Nevada, the proliferation of legalized gambling in other areas of the country has required state and local governments to look at other
=+b) Do you think the confidence interval noted in the report is valid? Briefly explain why or why not.
=+a) Discuss the assumptions and conditions for using Student’s t inference methods with these data.
=+and can also result in fines levied by the federal government. As required by government regulation, researchers continually monitor pollution levels. In the most recent test of pollution levels, 121 air samples were collected.The dust particulate levels must be reported to the federal
=+41. Growth and air pollution. Government officials have difficulty attracting new business to communities with troubled reputations. Nevada has been one of the fastest growing states in the country for a number of years.Accompanying the rapid growth are massive new construction projects. Since
=+Explain how you dealt with the outlier, and why.
=+. Cell phone batteries. A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal usage, their
=+b) The previous mean amount of time spent using the lab computer was 55 minutes. Find a 95% confidence interval for the true mean. What do you conclude about the claim?If there are outliers, find intervals with and without the outliers present.
=+a) Plot the data. Are any of the observations outliers?Explain.
=+39. Computer lab fees. The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes the amount of
=+b) Find a 99% confidence interval for the true percentage of flights that arrive late.
=+a) Check the assumptions and conditions for inference about the mean.
=+We can consider these data to be a representative sample of all months. There is no evidence of a time trend.
=+38. Late arrivals 2013. Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were late each month from 1995 through early 2013. Here’s a histogram, along with some summary statistics:10 15 20 25 Percent of
=+37. Departures 2011. What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are a histogram and summary statistics for the percentage of flights departing on time
=+d) How does the margin of error for the interval constructed in Exercise 35 compare with the margin of error constructed in this exercise? Explain statistically how sample size changes the accuracy of the constructed interval.Which sample would you prefer if you were the investigator? Why?
=+c) Find and interpret a 95% confidence interval.
=+b) What happens to the accuracy of the estimate when the interval is constructed using the smaller sample size?
=+36. Part-time jobs, part 2. Suppose the university in Exercise 35 sampled 16 students having part-time jobs instead of 51, and for the sample of 16, the sample mean salary again equaled $2350. Also assume the sample standard deviation is $425.
=+c) Explain what your interval means and provide an example of what it does not mean.
=+b) What assumptions have you made in this inference? Do you think the appropriate conditions have been satisfied?
=+a) Find a 95% confidence interval for the mean salary.
=+c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample?35. Part-time jobs. Many students have part-time jobs, ranging from a few hours per week to accommodate extra expenditure, to more intensive jobs to partially finance their study. A
=+b) Your classmate suggests that the margin of error in the interval could be reduced if the confidence level were changed to 90% instead of 95%. Do you agree with this statement? Why or why not?
=+a) Suppose the standard deviation of the values was 20 instead of the 11.26 used for that interval. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)?
=+34. Health status, part 2. In Exercise 32, we found a 95%confidence interval to estimate the average value of health status.
=+c) How could they achieve a confidence interval estimate that would better serve their planning needs?
=+b) How would the 95% confidence interval be worse for the planners?
=+a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be better for the city?(You need not actually create the new interval.)M11_SHAR8696_03_SE_C11.indd 389 14/07/14 7:30 AM 390 CHAPTER 11 Confidence
=+33. Parking, part 2. Suppose that for budget planning purposes the city in Exercise 31 needs a better estimate of the mean daily income from parking fees.
=+d) For all countries in the project, the average health index is 67.72. Do you think the average health index in Europe differs significantly from the overall average? Explain.
=+c) Interpret this interval and explain what 95% confidence means.
=+b) Find a 95% confidence interval for the mean value per European country.
=+a) What assumptions and conditions must be checked before finding a confidence interval for the mean? How would you check them?
=+32. Health status. In the OECD’s How’s life? project, health status, one of the 11 dimensions determining quality of life, depends on two data variables: life expectancy, and self-reported health. The 25 European countries in this study score an average of 67.04 on the index of selfreported
=+e) The consultant who advised the city on this project predicted that parking revenues would average $128 per day.Based on your confidence interval, what do you think of the consultant’s prediction? Why?
=+d) Explain what 90% confidence means in this context.
=+c) Explain in context what this confidence interval means.
=+b) Find a 90% confidence interval for the mean daily income this parking garage will generate.
=+a) What assumptions must you make in order to use these statistics for inference?
=+31. Parking. Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 44 weekdays, daily fees collected averaged $126, with a standard deviation of $15.
=+30. Credit card charges. A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. A histogram and boxplot are as follows:80 60 40 Frequency 20 January 2014 Charges 0 500,000 1,500,000 2,500,000 January 2014 Charges 0 500,000 1,500,000
=+29. CEO compensation. A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. The histogram and boxplot are as follows:0 10 20 30 40 50 60 70 510 15 Total Compensation in $ Million
=+d) 95% of all samples of employees will have average lunch costs between $780 and $920.e) We’re 95% sure that the average amount all employees pay for lunch is between $780 and $920.
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