Question: For the data in Exercise 8: a)

> Describe how the width of a 95% confidence interval for a mean changes as the sample size (n) increases, assuming the standard deviation remains the same.

> Describe how the width of a 95% confidence interval for a mean changes as the standard deviation (s) of a sample increases, assuming sample size remains the same.

> Using the t tables, software, or a calculator, estimate: a) the critical value of t for a 95% confidence interval with df = 7. b) the critical value of t for a 99% confidence interval with df = 102.

> Using the t-tables, software, or a calculator, estimate: a) the critical value of t for a 90% confidence interval with df = 17. b) the critical value of t for a 98% confidence interval with df = 88.

> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, reducing the margin of error will mean lower

> For the purchase amounts in Exercise 8: a) Construct a 90% confidence interval for the mean purchases of all customers, assuming that the assumptions and conditions for the confidence interval have been met. b) How large is the margin of error? c) How

> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, higher confidence means a smaller margin of e

> Two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads—that’s 56%. That makes the 90% confidence interval (51%, 61%). What does this mean? Are the conclusions in parts a–e correct? Explain your answers. a) Betwe

> A catalog sales company promises to deliver orders placed on the Internet within 3 days. Followup calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% { 6%. What does t

> It’s believed that 4% of children have a gene that may be linked to type 1 diabetes. Researchers hoping to track 20 of these children for several years test 732 newborns for the presence of this gene. What’s the probability that they find enough subjects

> When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fa

> Information on a packet of seeds claims that the germination rate is 92%. What’s the probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to discuss your assumptions and check the conditions that support your model.

> Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters. What’s the probability the newspaper’s sample wi

> After hearing of the national result that 44% of students engage in binge drinking (5 drinks at a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in t

> Based on the 80% national retention rate described in Exercise 37, does a college where 551 of the 603 freshmen returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.

> A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). Use the 68–95–99.7 Rule to describe the sampling distribution model for the proportion of students in a randomly selected group of

> For the ages in Exercise 7: a) Construct a 95% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the confidence interval have been met. b) How large is the margin of error? c) How would the confide

> Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2012 the company reported that the national college freshman-to-sophomore retention rate at four-year colleges was about 80.0%. Consider colleges wi

> The campus representative for Lens.com wants to know what percentage of students at a university currently wear contact lens. Suppose the true proportion is 30%. a) We randomly pick 100 students. Let pn represent the proportion of students in this sampl

> Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. a) What are the mean and standard deviation of the proportion of clients in this group who may no

> In early 2013 Realty Trac reported that foreclosures had settled down to 1 in 859 homes per month for a rate of 0.116%, far below the 1.6% seen during the financial crisis of 2007–2008. Suppose a large bank holds 9455 of these mortgages. a) Can you use

> It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children. a) Can you use the Normal Model to describe the sampling distribution model for the sample proportion o

> The Centers for Disease Control and Prevention (www.cdc.gov/tobacco/data_statistics/fact_ sheets/adult_data/cig_smoking/index.htm) reported that in 2016, 15.5% of American adults smoked cigarettes. Describe the sampling distribution model for the proport

> State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 80 cars. a) Using the 68–95–99.7 Rule, draw and label the distribution of the proportio

> Even more quality. In a really large bag of M&M’s, we found 12% of 500 candies were green. Is this evidence that the manufacturing process is out of control and has made too many greens? Explain.

> One student in the class of Exercise 25 claims to have found a winning strategy. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, 58% were w

> Would a bigger sample help us to assess manufacturing consistency? Suppose instead of the 50-candy bags of Exercise 26, we work with bags that contain 200 M&M’s each. Again we calculate the proportion of green candies found. a) Explain why it’s appropri

> Find the critical value t* for: a) a 90% confidence interval based on 19 df. b) a 90% confidence interval based on 4 df.

> The class in Exercise 25 expands its stock-picking experiment. a) The students use computer-generated random numbers to choose 25 stocks each. Use the 68–95–99.7 Rule to describe the sampling distribution model. b) Confirm that you can use a Normal mod

> Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Sometimes, however, we can find a simple example. The candy company that makes M&M’s candies claims that 10% o

> In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of “success

> The automatic character recognition device discussed in Exercise 22 successfully reads about 85% of handwritten loan applications. In Exercise 22 you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size

> The philanthropic organization in Exercise 21 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 21 you looked at the histograms showing distributions of sample proportions from 1000 simula

> WinCo Foods, a large discount grocery retailer in the western United States, promotes itself as the lowest priced grocery retailer. In newspaper ads WinCo Foods published a price comparison for products between WinCo and several competing grocery retaile

> Commercial airlines overbook f lights, selling more tickets than they have seats, because a sizable number of reservation holders don’t show up in time for their f lights. But sometimes, there are more passengers wishing to board than t

> For another test of the tires in Exercise 79, the company tried them on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the following table. a) Find a 95% confidence interval for the m

> In an experiment on braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 miles per hour. Twenty tests were run, 10 each on both dry and wet pavement, with r

> Real estate agents want to set correctly the price of a house that’s about to go on the real estate market. They must choose a price that strikes a balance between one that is so high that the house takes too long to sell and one that’s so low that not e

> Find the critical value t* for: a) a 95% confidence interval based on 24 df. b) a 95% confidence interval based on 99 df.

> A leading manufacturer of exercise equipment wanted to collect data on the effectiveness of their equipment. An August 2001 article in the journal Medicine and Science in Sports and Exercise compared how long it would take men and women to burn 200 calor

> A small company, on hearing about the employee athlete program (see Exercise 75) at the large company down the street, decides to try it as well. To measure the difference in productivity, they measure the average number of keystrokes per hour of 23 empl

> An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an “employee athlete” program, encouraging every employee to devote 5

> Exercises 70 and 72 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed. Exercises 70: Alternative sources of energ

> Exercises 69 and 71 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company. Exerc

> In Exercise 70, we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricity-generating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind s

> In Exercise 69, we saw summary statistics for 10 drivers’ car insurance premiums quoted by a local agent and an online company. Here are displays for each company’s quotes and for the difference (Local â€&#1

> Alternative sources of energy are of increasing interest throughout the energy industry. Wind energy has great potential. But appropriate sites must be found for the turbines. To select the site for an electricitygenerating wind turbine, wind speeds were

> After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving r

> It has long been a dream of farmers to summon rain when it is needed for their crops. Crop losses to drought have significant economic impact. One possibility is cloud seeding, in which chemicals are dropped into clouds in an attempt to induce rain. Simp

> For the regression of Exercise 2, find the standard error of the regression slope. Show all three values that go into the calculation. Exercise 2: A training center, wishing to demonstrate the effectiveness of their methods, tests some of their clients

> For the same reasons identified in Exercise 42, a friend of yours claims that the attendance at Road (away) games is lower in the American League than in the National League. Using the Attendance 2016 data (same data as in Exercises 42 and 44), you decid

> An investment blog suggests that you’ve been doing this all wrong and should invest in mutual funds only for the short term. So you decide to compare returns at 1 month and 3 months. a) Using the data provided, check the conditions for this test. b) Writ

> You have heard that if you leave your money in mutual funds for a longer period of time, you will see a greater return. So you would like to compare the 1-year and 5-year returns of a random sample of mutual funds to see if indeed, your return is expecte

> Using the results of the experiment described in Exercise 63, does it matter whether one listens to rap music while studying, or is it better to study without music at all? a) Test an appropriate hypothesis and state your conclusion. b) If you concluded

> A company is considering marketing their classical music as “music to study by.” Is this a valid slogan? In a study conducted by some statistics students, 62 people were randomly assigned to listen to rap music, music

> Given the test results on golf tees described in Exercise 61, is there evidence that balls hit off Stinger tees travel farther? Assume that 6 balls were hit off each tee and that the data are suitable for inference.

> Does it matter what kind of tee a golfer places the ball on? The company that manufactures “Stinger” tees claims that the thinner shaft and smaller head will lessen resistance and drag, reducing spin and allowing the b

> Financial analysts know that January credit card charges will generally be much lower than those of the month before. What about the difference between January and the next month? Does the trend continue? The dataset contains the monthly credit card char

> Spending on credit cards decreases after the Christmas spending season (as measured by amount charged on a credit card in December). The dataset with the same name as this exercise contains the monthly credit card charges of a random sample of 99 cardhol

> The Internet has revolutionized business and offers unprecedented opportunities for globalization. However, the ability to access the Internet varies greatly among different regions of the world. One of the variables the United Nations collects data on e

> Games for the iPad have a distribution of prices that is skewed to the high end. a) Explain why this is what you would expect. b) Members of the iPad gamers club each own about 50 games. Pat is one such member. What would you expect the shape of the di

> Examine the regression and scatterplot showing the regression line, 95% confidence intervals, and 95% prediction intervals using 2006 and 2010 energy use (kg oil equivalent per $1000 GDP) for a sample of 31 countries first examined in Exercise 54. The re

> Here is a scatterplot showing the regression line, 95% confidence intervals, and 95% prediction intervals, using 2015 and 2016 male unemployment data for a sample of 33 nations. The response variable is the 2016-Male Rate, and the predictor variable is t

> Here is a scatterplot showing the regression line, 95% confidence intervals, and 95% prediction intervals, using youth unemployment data for a sample of 33 nations. The response variable is the Male Rate, and the predictor variable is the Female Rate.

> The Great Recession of 2008 changed spending and energy use habits worldwide. Based on data collected from the United Nations Millennium Indicators Database related to measuring the goal of ensuring environmental sustainability, investigate the associati

> A sample of 61 model-2013 cars from an online information service was examined to see how fuel efficiency (as highway mpg) relates to the cost (Manufacturer’s Suggested Retail Price in dollars) of cars. (Data in All the efficiency) Here

> The analyst in Exercise 28 realized the data were in need of transformation because of the non-linearity between the variables. Economists commonly take the logarithm of these variables to make the relationship more nearly linear, and she did too. (These

> Using the same data provided in Exercise 48, answer the following questions. a) Find the 95% prediction interval for the effectiveness of the video on a pitcher with an initial ability of 33 strikes. b) Do you think predictions made by this regression wi

> Consider the high school SAT scores data from Exercise 31 once more. The mean Verbal score was 596.30 and the standard deviation was 99.52. a) Find a 90% confidence interval for the mean SAT Math score for all students with an SAT Verbal score of 500.

> Consider again the data in Exercise 29 about the fuel economy and weights of cars. a) Create a 95% confidence interval for the average fuel efficiency among cars weighing 2500 pounds, and explain what your interval means. b) Create a 95% prediction inte

> Ads for a Little League instructional video claimed that the techniques would improve the performances of Little League pitchers. To test this claim, 20 Little Leaguers threw 50 pitches each, and we recorded the number of strikes. After the players parti

> For each situation below identify the population and the sample and identify p and pn if appropriate and what the value of pn is. Would you trust a confidence interval for the true proportion based on these data? Explain briefly why or why not. a) As co

> Many factors may affect fans’ decision to go to a ball game. Is it possible that fans prefer teams with an older pitching staff? a) Examine a scatterplot of Attend/Game and PitchAge. Check the conditions for regression. b) Do you think there is a linear

> In Exercise 44, the company Zappos was omitted. Here is a scatterplot of the data with Zappos plotted as an x: a) In words, what does the outlying point say about Zappos? b) What effect would this point have on the regression, had it been left with t

> In Exercise 43, we examined the Worldwide Cost of Living Survey cost of living index. Now we use the Restaurant Price Index to predict total cost of living. Here are the results: a) How do you interpret the coefficient of Restaurant price? b) The R2 o

> Fortune Magazine publishes the top 100 companies to work for every year. Among the information listed is the percentage growth in jobs at each company. The output below shows the regression of job growth (%) in the current year on job growth from two yea

> The Worldwide Cost of Living Survey published by Numbeo.com provides an index that expresses the cost of living in other cities as a percentage of the New York cost. For example, in 2017, the cost of living index in Geneva was 142, which means that it wa

> There are 168 hours in a week. If you spend all of it sleeping and having fun, you will earn very little money. On the other hand, if you spend much of it working, do you earn more? In other words, do people earn more money each year when they work a gre

> In 2014, cnet.com listed the battery life (in hours) and maximum luminous intensity (i.e., screen brightness, in cd>m2) for a sample of tablet computers. We want to know if we can predict battery life from the maximum brightness. (reviews.cnet.com/830

> Using a statistics program, consider again the relationship between the sales and profits of Fortune 500 companies that you analyzed in Exercise 38. a) Find a 95% confidence interval for the slope of the regression line. Interpret your interval in conte

> Using a statistics program, consider again the relationship between the population and ozone level of U.S. cities that you analyzed in Exercise 37. a) Give a 90% confidence interval for the approximate increase in ozone level associated with each additi

> A business analyst was interested in the relationship between a company’s sales and its profits. She collected data (in millions of dollars) from a random sample of Fortune 500 companies and created the regression analysis and summary s

> A market researcher for a provider of iPhone accessories wants to know the proportion of customers who own cars to assess the market for a new iPhone dashboard mount. A survey of 500 customers indicates that 76% own cars. a) What is the standard deviati

> The Environmental Protection Agency is examining the relationship between the ozone level (in parts per million) and the population (in millions) of U.S. cities. Part of the regression analysis is shown. a) We suspect that the greater the population o

> Consider the high school SAT scores data from Exercise 31. a) Find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores. b) Explain in this context what your confidence interval means.

> Consider again the data in Exercise 29 about the gas mileage and weights of cars. a) Create a 95% confidence interval for the slope of the regression line. b) Explain in this context what your confidence interval means.

> The Gallup organization has, over six decades, periodically asked the following question: If your party nominated a generally well-qualified person for president who happened to be a woman, would you vote for that person? We wonder if the proportion of t

> Football owners are constantly in competition for good players. The more wins, the more likely that the team will provide good business returns for the owners. The resources that each of the 32 teams has in the National Football League (NFL) vary, but th

> How strong is the association between labor productivity and labor costs? Data from the Bureau of Labor Statistics for labor productivity, as measured by Output per Employee, and Unit Labor Costs across industries, are used to examine this relationship (

> How strong was the association between student scores on the Math and Verbal sections of the old SAT? Scores on this exam ranged from 200 to 800 and were widely used by college admissions offices. Here are summary statistics, regression analysis, and plo

> Consumer Reports listed the price (in dollars) and power (in cold cranking amps) of auto batteries. We want to know if more expensive batteries are generally better in terms of starting power. Here are the regression and residual output, where the respon

> A consumer organization has reported test data for 50 car models. We will examine the association between the weight of the car (in thousands of pounds) and the fuel efficiency (in miles per gallon). Use the data provided on the disk to answer the follow

> A business analyst is looking at a company’s assets and sales to determine the relationship (if any) between the two measures. She has data (in $million) from a random sample of 79 Fortune 500 companies, and obtained the linear regressi

> A marketing researcher for a phone company surveys 100 people and finds that that proportion of clients who are likely to switch providers when their contract expires is 0.15. a) What is the standard deviation of the sampling distribution of the proport

> Based on the analysis of used car prices you did for Exercise 25, if appropriate, create a 95% confidence interval for the slope of the regression line and explain what your interval means in context.

> The following software results provide information about the size (in square feet) of 18 homes in Ithaca, New York, and the city’s assessed value of those homes, where the response variable is Assessment. a) Explain why inference for

> Classified ads in a newspaper offered several used Toyota Corollas for sale. Listed below are the ages of the cars and the advertised prices. a) Make a scatterplot for these data. b) Do you think a linear model is appropriate? Explain. c) Find the e

> Using unemployment data provided by the World Bank, investigate the association between the male unemployment rate in 2014 and 2017. a) Find a regression model predicting the 2017 rate from the 2014 rate. b) Examine the residuals to determine if a line

> The index of deflated turnover for retail trade shows the activity in volume of the retail trade sector. The United Nations Statistics Division reports Retail trade deflated sales/turnover (seasonally adjusted) with 2005 = 100. The data file holds this i

> The Brief Case for Chapter 4 listed the rate of return for 98 mutual funds over the previous 3-year and 5-year periods. It’s common for advertisements to carry the disclaimer that “past returns may not be indicative of future performance.” Do these data