Question: A company has developed a new diet

> Beer bottles are filled so that they contain an average of 330 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 4 ml. a. What is the probability that a randomly selected bottle wi

> According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probabilit

> You score 90 on the midterm, 60 on the final, and 80 on the class project. What is your average score if the midterm is worth 30%, the final is worth 50%, and the class project is worth 20%?

> The following table presents a portion of the annual returns for two mutual funds offered by the investment giant Fidelity. The Fidelity Select Automotive Fund invests primarily in companies engaged in the manufacturing, marketing, or sales of automobile

> A social scientist wants to analyze the relationship between educational attainment and salary. He interviews eight people. The accompanying table shows each person’s years of higher education (Education in years) and corresponding sala

> The following table shows the annual returns (in %) for T. Rowe Price’s Value and International Stock funds for the time period 2005–2009. a. Calculate and interpret the covariance between the returns. b. Calculate a

> A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. b. What is the probability that the sample

> A random sample of size n = 100 is taken from a population with mean μ = 80 and standard deviation σ = 14. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. b. What is the probability that the sample

> Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 10% of produced items are known to be nonconform

> The producer of a particular brand of soup claims that its sodium content is 50% less than that of its competitor. The food label states that the sodium content measures 410 milligrams per serving. Assume the population of sodium content is normally dist

> According to a report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy (The New York Times, July 1, 2010). Assume 150 patients decide to get their genomes sequenced. a. If th

> A random sample is drawn from a normally distributed population with mean μ = 12 and standard deviation σ = 1.5. a. Comment on the sampling distribution of the sample mean with n = 20 and n = 40. b. Can you use the standard normal distribution to calcula

> Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey show that annual expenditures for cellular phone services per consumer unit increased from $210 in 2001 to $608 in 2007. Let the standard deviation of annual cellular expenditure be $4

> Georgia residents spent an average of $470.73 on the lottery in 2010, or 1% of their personal income (www.msn.com, May 23, 2012). Suppose the amount spent on the lottery follows a normal distribution with a standard deviation of $50. a. What is the proba

> Texas is home to more than one million undocumented immigrants, and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfi

> Trader Joe’s is a privately held chain of specialty grocery stores in the United States. Starting out as a small chain of convenience stores, it has expanded to over 340 stores as of June 2010 (www.traderjoes.com). It has developed a reputation as a uniq

> An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean μ = 80 cm and a standard deviation σ = 2 cm. a. Find the probability that the length of one randomly sele

> While starting salaries have fallen for college graduates in many of the top hiring fields, there is some good news for business undergraduates with concentrations in accounting and finance (Bloomberg Businessweek, July 1, 2010). According to the Nationa

> Presidential job approval is the most-watched statistic in American politics. According to the June 2010 NBC/Wall Street Journal public opinion poll, President Barack Obama had reached his lowest approval rating since taking office in January of 2009. Th

> According to the Bureau of Labor Statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2, 2008). Assume that the probability distributions are nor

> The college admissions office at a local university usually admits 750 students and knows from previous experience that 25% of these students choose not to enroll at the university. a. Construct the centerline and the upper and lower control limits for

> A firm produces computer chips for personal computers. From past experience, the firm knows that 4% of the chips are defective. The firm collects a sample of the first 500 chips manufactured at 1:00 pm for the past two weeks. The following sample proport

> A manufacturing process produces steel rods in batches of 1,000. The firm believes that the percent of defective items generated by this process is 5%. a. Construct the centerline and the upper and lower control limits for the chart. b. An engineer inspe

> Fast bowling, also known as pace bowling, is an important component of the bowling attack in the sport of cricket. The objective is to bowl at a high speed and make the ball turn in the air and off the ground so that it becomes difficult for the batsman

> A production process is designed to fill boxes with an average of 14 ounces of cereal. The population of filling weights is normally distributed with a standard deviation of 2 ounces. Inspectors take periodic samples of 10 boxes. The following sample mea

> The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. Month …………………………………………………………………………… Closing Stock Price January ………………………………………………………………………………………

> Major League Baseball Rule 1.09 states that “the baseball shall weigh not less than 5 or more than 5¼ ounces” (www.mlb.com). Use these values as the lower and the upper control limits, respectively. Assum

> Random samples of size n = 400 are taken from a population with p = 0.10. a. Construct the centerline and the upper and lower control limits for the chart. b. Suppose six samples of size 400 produced the following sample proportions: 0.06, 0.11, 0.09, 0.

> Random samples of size n = 500 are taken from a population with p = 0.34. a. Construct the centerline and the upper and lower control limits for the chart. b. Suppose six samples of size 500 produced the following sample proportions: 0.28, 0.30, 0.33, 0.

> The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008. Based on the 2006 compensation data obtained from the Securities and Exchange Com

> A study finds that companies are setting aside a large chunk of their IT spending for green technology projects (BusinessWeek, March 5, 2009). Two out of three of the large companies surveyed by Deloitte said they have at least 5% of their IT budget earm

> A random sample of size n = 80 is taken from a population of size N = 600 with a population proportion p = 0.46. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the samp

> A random sample of size n = 100 is taken from a population of size N = 3,000 with a population proportion of p = 0.34. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of th

> A random sample of size n = 70 is taken from a finite population of size N = 500 with mean μ = 220 and variance σ2 = 324. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of

> A random sample of size n = 100 is taken from a population of size N = 2,500 with mean μ = −45 and variance σ2 = 81. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the

> According to a FCC survey, one in six cell phone users has experienced “bill shock” from unexpectedly high cell phone bills (Tech Daily Dose, May 26, 2010). a. Discuss the sampling distribution of the sample proportion based on a sample of 200 cell phone

> The following table shows the annual returns (in percent) for Fidelity’s Electronics and Utilities funds. a. Derive the 99% confidence intervals for the mean returns for Fidelity’s Electronics and Utilities funds. b.

> Discuss the consequences of Type I and Type II errors for each of the claims considered in the preceding question.

> Define the consequences of Type I and Type II errors for each of the tests considered in the preceding question.

> Which of the following statements are correct? Explain if incorrect. a. “I accept the null hypothesis since sample evidence is not inconsistent with the null hypothesis.” b. “Since sample evidence cannot be supported by the null hypothesis, I reject the

> Explain why the following statements are not correct. a. “With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error.” b. “I have already decided how much of the Type I error I am g

> Residents of Hawaii have the longest life expectancies in the United States, averaging 81.48 years (www.worldlifeexpectancy.com; data retrieved June 4, 2012). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. a.

> A report suggests that business majors spend the least amount of time on course work than do all other college students (The New York Times, November 17, 2011). A provost of a university conducts a survey of 50 business and 50 nonbusiness students. Stude

> The euro-zone crisis has wreaked havoc on U.S. stock markets (The Wall Street Journal, June 8, 2012). A portfolio analyst wonders if the average trading volume on the Dow Jones Industrial Average (DJIA) has decreased since the beginning of the year. She

> The Great Recession cost America trillions of dollars in lost wealth and also levied a heavy toll on the national psyche (The Wall Street Journal, December 21, 2009). According to a poll, just 33% of those surveyed said America was headed in the right di

> Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23, 2010). According to Freddie Mac, the average rate for 30-year fixed loans for the week was 4.37%. An economist wants to test if there is any change in th

> Hockey pucks used by the National Hockey League (NHL) and other professional leagues weigh an average of 163 grams (5.75 ounces). A quality inspector monitors the manufacturing process for hockey pucks. She takes eight samples of n = 10. It is believed t

> A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 20 minutes. A sample of 32 main roa

> An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recent

> A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Would the manager of the pharmaceutical

> According to a report on workforce diversity, about 60% of the employees in high-tech firms in Silicon Valley are white and about 20% are Asian (www.money.cnn.com, November 9, 2011). Women, along with blacks and Latinos, are highly underrepresented. Just

> A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to want to see the movie ag

> Research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, 2008). The report documents that 70% of older workers in England feel fulfilled, compared with just 50% of younger workers. A demographer believe

> The margarita is one of the most common tequila-based cocktails, made with tequila mixed with triple sec and lime or lemon juice, often served with salt on the glass rim. A common ratio for a margarita is 2:1:1, which includes 50% tequila, 25% triple sec

> Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.05 and at α = 0.10?

> Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?

> According to a report, college graduates in 2010 were likely to face better job prospects than 2009 graduates (The New York Times, May 24, 2010). Many employers who might have been pessimistic at the start of the 2009–2010 academic year were making more

> An article found that Massachusetts residents spent an average of $860.70 on the lottery in 2010, more than three times the U.S. average (www.businessweek.com, March 14, 2012). A researcher at a Boston think tank believes that Massachusetts residents spe

> A police officer is concerned about speeds on a certain section of Interstate 95. The data accompanying this exercise show the speeds of 40 cars on a Saturday afternoon. a. The speed limit on this portion of Interstate 95 is 65 mph. Specify the competing

> A study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The data accompanying this exercise show the average debt payments (Debt, in $) for 26 metropolitan areas, a portion of which is shown in the

> One of the consequences of the Great Recession was a free fall of the stock market’s average price/earnings ratio, or P/E ratio (The Wall Street Journal, August 30, 2010). Generally, a high P/E ratio suggests that investors are expecting higher earnings

> In September 2007, U.S. home prices fell at a record pace, and price declines in Los Angeles and Orange counties in California outpaced other major metropolitan areas (Los Angeles Times, November 28, 2007). The report was based on the Standard & Poor’s/C

> Economists (NABE), the U.S. gross domestic product (GDP) will expand by 3.2% in 2011 (The Wall Street Journal, May 23, 2010). Suppose the sample standard deviation of their predictions was 1%. At the 5% significance level, test if the mean forecast GDP o

> A local brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard d

> Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (The New York Times, July 20, 2008). Some of the biggest companies are wary of the new breed of computers because their low price could threaten PC makersâ

> The manager of a small convenience store does not want her customers standing in line for too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than fiv

> Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?

> Executive compensation has risen dramatically compared to the rising levels of an average worker’s wage over the years. Sarah is an MBA student who decides to use her statistical skills to estimate the mean CEO compensation in 2010 for all large companie

> Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?

> On average, a college student graduates with $27,200 in debt (The Boston Globe, May 27, 2012). A researcher collects data on debt from 40 recent undergraduates from Connecticut. Assume that the population standard deviation is $5,000. a. The researcher b

> A realtor in Mission Viejo, California, believes that the average price of a house is more than $500,000. a. State the null and the alternative hypotheses for the test. b. The data accompanying this exercise show house prices. (Data are in $1,000s.) c. A

> A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion f

> In May 2008, CNN reported that sports utility vehicles (SUVs) are plunging toward the “endangered” list. Due to the uncertainty of oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a

> It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars

> The sudoku puzzle has become very popular all over the world. It is based on a 9 × 9 grid and the challenge is to fill in the grid so that every row, every column, and every 3 × 3 box contains the digits 1 through 9. A researcher is interested in estimat

> Consider the following hypotheses: A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2. a. Calculate the p-value. What is the conclusion if &Icir

> A consumer group has accused a restaurant of using higher fat content than what is reported on its menu. The group has been asked to conduct a hypothesis test to substantiate its claims. a. Is the manager of the restaurant more concerned about a Type I e

> The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 98% of the people who have that disease. However, it erroneously gives a positi

> The manager of a large manufacturing firm is considering switching to new and expensive software that promises to reduce its assembly costs. Before purchasing the software, the manager wants to conduct a hypothesis test to determine if the new software d

> A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let th

> For a continuous random variable X with an upper bound of 4, P (0 ≤ X ≤ 2.5) = 0.54 and P (2.5 ≤ X ≤ 4) = 0.16. Calculate the following probabilities. a. P (X < 0) b. P (X > 2.5) c. P (0 ≤ X ≤ 4)

> The cumulative probabilities for a continuous random variable X are P (X ≤ 10) = 0.42 and P (X ≤ 20) = 0.66. Calculate the following probabilities. a. P (X > 10) b. P (X > 20) c. P (10 < X < 20)

> Consider the following cumulative probability distribution. a. Calculate P (X &acirc;&#137;&curren; 3). b. Calculate P (X = 3). c. Calculate P (2 &acirc;&#137;&curren; X &acirc;&#137;&curren; 4). X 1 2 4 P (X<x) 0.15 0.35 0.52 0.78 0.84 1 LO

> Consider the following discrete probability distribution a. Complete the probability distribution. b. Graphically depict the probability distribution and comment on the symmetry of the distribution. c. What is the probability that the random variable X

> Consider the following discrete probability distribution. // a. Is this a valid probability distribution? Explain. b. Graphically depict this probability distribution. c. What is the probability that the random variable X is less than 40? d. What is t

> A variety of packaging solutions exist for products that must be kept within a specific temperature range. A cold chain distribution is a temperature-controlled supply chain. An unbroken cold chain is an uninterrupted series of storage and distribution a

> Apple products have become a household name in America, with 51% of all households owning at least one Apple product (CNN, March 19, 2012). a. What is the probability that two in a random sample of four households own an Apple product? b. What is the pr

> The following table shows the annual returns (in percent) for Fidelity&acirc;&#128;&#153;s Electronic and Utilities funds. a. Calculate the sample mean, the sample variance, and the sample standard deviation for each fund. b. Which fund had the higher

> A professor uses a relative scale for grading. She announces that 60% of the students will get at least a B, with 15% getting A’s. Also, 5% will get a D and another 5% will get an F. Assume that no incompletes are given in the course. Let Score be define

> Jane Wormley is a professor of management at a university. She expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5% chance that she may not be able to fund any student, there

> Census. The accompanying data file shows, among other variables, median household income and median house value for the 50 states in 2010. Assume that income and house value data are bell-shaped. a. Use z-scores to determine if there are any outliers in

> Data are drawn from a bell-shaped distribution with a mean of 5 and a standard deviation of 2.5. a. Approximately what percentage of the observations are positive? b. Approximately what percentage of the observations are not positive?

> The manager at a water park constructed the following frequency distribution to summarize attendance in July and August. Attendance ……………………………………………………………………………………. Frequency 1,000 up to 1,250 …………………………………………………………………………………………. 5 1,250 up to 1,500 ………

> The following table reports the number of people as well as the number of people living below the poverty level across regions in the U.S. for the year 2013. (All numbers are in 1,000s.) a. Graph and interpret the pie chart that summarizes the proporti

> A data set has a mean of 1,500 and a standard deviation of 100. a. Using Chebyshev’s theorem, what percentage of the observations fall between 1,300 and 1,700? b. Using Chebyshev’s theorem, what percentage of the observations fall between 1,100 and 1,9

> The Statistical Abstract of the United States, 2010 provided the following frequency distribution of the number of people (in 1,000s) who live below the poverty level by region. Region ……………………………………………………………………………… Number of People Northeast …………………………

> According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume that the survey was based on a random sample of 36 high school girls. The sample standard deviation is computed as 10 text messages

> The one-year return (in %) for 24 mutual funds is as follows: a. Construct the frequency distribution using classes of &acirc;&#136;&#146;20 up to &acirc;&#136;&#146;10, &acirc;&#136;&#146;10 up to 0, etc. b. Construct the relative frequency, the cumu

> A survey conducted by CBS News asked parents about the professions they would want their children to pursue. Parents’ preferences (in %) are summarized in the following table. Profession ………………………………………………………………………... Parents’ Preference Doctor, banker,

> Patrons at a local restaurant were asked to rate their recent experience at the restaurant with respect to its advertised atmosphere of upbeat, comfortable, and clean. Possible responses included Outstanding, Good, OK, and Horrible. The following table s