A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. a. Set up the null and the alternative hypotheses to determine if the machine is working improperly—that is, it is either under filling or overfilling the cereal boxes. b. Calculate the value of the test statistic and the p-value. c. At the 5% level of significance, can you conclude that the machine is working improperly? Explain.
> The accompanying figure plots the monthly stock price of Caterpillar, Inc., from July 2009 through March 2011. The stock has experienced tremendous growth over this time period, almost tripling in price. Does the figure reflect this growth? If not, why n
> In a USA TODAY/Gallup Poll, respondents favored Barack Obama over Mitt Romney in terms of likeability, 60% to 30% (Los Angeles Times, July 28, 2012). The following bar chart summarizes the responses. a. What percentage of respondents favored neither Ob
> A professor records the majors of her 30 students as follows: a. What is the measurement scale of these data? b. Summarize the results in tabular form. c. What information can be extracted from the data? Accounting Economics Undecided Finance Man
> In each of the following scenarios, define the type of measurement scale. a. A meteorologist records the amount of monthly rainfall over the past year. b. A sociologist notes the birth year of 50 individuals. An investor monitors the daily stock price
> In each of the following scenarios, define the type of measurement scale. a. An investor collects data on the weekly closing price of gold throughout a year. b. An analyst assigns a sample of bond issues to one of the following credit ratings, given in
> In each of the following scenarios, define the type of measurement scale. a. A kindergarten teacher marks whether each student is a boy or a girl. b. A ski resort records the daily temperature during the month of January. c. A restaurant surveys its cu
> Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous. a. Colors of cars in a mall parking lot. b. Time it takes each student to complete
> Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous. a. Points scored in a football game. b. Racial composition of a high school class
> Conduct an online search for a weekly car rental in Seattle, Washington, and Portland, Oregon, for different car types and rental car companies for the year 2017. Are the data structured or unstructured? Are the data cross-sectional or time series?
> Ask your peers about their online social media usage. In particular collect information on (a) whether they use Facebook, Instagram, and Snapchat, (b) how often they use each social media service, and (c) their overall satisfaction with each of these ser
> A data set has a mean of 500 and a standard deviation of 25. a. Using Chebyshev’s theorem, find the interval that encompasses at least 75% of the data. b. Using Chebyshev’s theorem, find the interval that encompasses at least 89% of the data.
> Conduct an online search to compare price and fuel economy of small hybrid vehicles such as Toyota Prius, Ford Fusion, and Chevrolet Volt. Would the resulting data be structured or unstructured? Explain
> Go to The New York Times website at www.nytimes.com/ and review the front page. Would you consider the data on the page to be structured or unstructured? Explain.
> An investor bought common stock of Apple Inc. on three occasions at the following prices. Date Price …………………………………………………………………………………… Per Share January 2016 …………………………………………………………………………………….. 94.81 July 2016 ………………………………………………………………………………………… 102.67 Dec
> A local restaurant is committed to providing its patrons with the best dining experience possible. On a recent survey, the restaurant asked patrons to rate the quality of their entrées. The responses ranged from 1 to 5, where 1 indicated a d
> The significant decline of savings in the United States from the 1970s and 1980s to the 1990s and 2000s has been widely discussed by economists (www.money.cnn.com, June 30, 2010). According to the Bureau of Economic Analysis, the savings rate of American
> The following table lists a portion of U.S. life expectancy (in years) for the 50 states. Life Expectancy by State, 2010–2011 Source: en.wikipedia.org/wiki/List_of_U.S._states_by_life_expectancy, data retrieved April 25, 2012. In a r
> There are six broad sectors that comprise the Dow Jones Industrial Average (DJIA). These are the areas in which the company conducts its primary business. The following table shows a portion of the 30 companies that comprise the DJIA and each company’s s
> Research suggests that depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a study involving 949 elderly persons, it was reported that 22% of those who had depression went on to develop dementia,
> Business graduates in the United States with a marketing concentration earn high salaries. According to the Bureau of Labor Statistics, the average annual salary for marketing managers was $140,660 in 2015. a. What is the relevant population? b. Do you
> Many people regard video games as an obsession for youngsters, but, in fact, the average age of a video game player is 35 years (Reuters.com, August 21, 2009). Is the value 35 likely the actual or the estimated average age of the population? Explain
> The minimum and maximum observations in a population are 20 and 80, respectively. What is the minimum sample size n required to estimate μ with 80% confidence if the desired margin of error is E = 2.6? What happens to n if you decide to estimate μ with 9
> It came as a big surprise when Apple’s touch screen iPhone 4, considered by many to be the best smartphone ever, was found to have a problem (The New York Times, June 24, 2010). Users complained of weak reception, and sometimes even dropped calls, when t
> Thirty-three percent of children and teens in the United States are obese or overweight (Health, October 2010). A health practitioner in the Midwest collects data on 200 children and teens and finds that 84 of them are either obese or overweight. a. The
> An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island. a. State the null and the alternative hypotheses in order to test whether average sales differ from $130,000. b. Calculate the value of the test statistic and
> On average, Americans drive 13,500 miles per year (The Boston Globe, June 7, 2012). An economist gathers data on the driving habits of 50 residents in the Midwest. a. The economist believes that the average number of miles driven annually by Midwesterner
> Using data from the past 25 years, an investor wants to test whether the average return of Vanguard’s Precious Metals and Mining Fund is greater than 12%. Assume returns are normally distributed with a population standard deviation of 30%. a. State the n
> A survey finds that 17% of Americans cannot part with their landlines (The Washington Post, February 27, 2014). A researcher in the rural South collects data from 200 households and finds that 45 of them still have landlines. a. The researcher believes t
> A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its
> A national survey found that 33% of high school students said they texted or e-mailed while driving (The Boston Globe, June 8, 2012). These findings came a day after a Massachusetts teenager was convicted for causing a fatal crash while texting. A resear
> A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers. Management will take corrective actions if t
> A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch screen phone is more expensive, its battery life is more tha
> One in five 18-year-old Americans has not graduated from high school (The Wall Street Journal, April 19, 2007). A mayor of a North-eastern city comments that its residents do not have the same graduation rate as the rest of the country. An analyst from t
> With increasing out-of-pocket healthcare costs, it is claimed that more than 60% of senior citizens are likely to make serious adjustments to their lifestyle. Test this claim at the 1% level of significance if in a survey of 140 senior citizens, 90 repor
> Construct the null and the alternative hypotheses for the following claims: a. “I am going to get the majority of the votes to win this election.” b. “I suspect that your 10-inch pizzas are, on average, less than 10 inches in size.” c. “I will have to fi
> A politician claims that he is supported by a clear majority of voters. In a recent survey, 24 out of 40 randomly selected voters indicated that they would vote for the politician. Is the politician’s claim justified at the 5% level of significance?
> Research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008). Even web-savvy surfers could find
> In order to endure financial hardships such as unemployment and medical emergencies, Americans have increasingly been raiding their already fragile retirement accounts (MSN Money, July 16, 2008). It is reported that between 1998 and 2004, about 12% of fa
> A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy an
> You would like to determine if more than 50% of the observations in a population are below 10. At α = 0.05, conduct the test on the basis of the following 20 sample observations: 8 12 14 11 7 8 12 6 8 9 6 11 4 13 10 3. LO
> You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. Implement the test at the 1% level of significance.
> In order to test if the population proportion is greater than 0.65, you draw a random sample of 200 observations and obtain a sample proportion of 0.72. a. Specify the competing hypotheses. b. Is the normality condition satisfied? Explain. c. Calculate t
> In order to conduct a hypothesis test for the population proportion, you sample 320 observations that result in 128 successes. Conduct the following tests at α = 0.05. a. H0: p ≥ 0.45; HA: p < 0.45 b. H0: p = 0.45; HA: p ≠ 0.45
> A recent survey asked 5,324 individuals: What’s most important to you when choosing where to live? The responses are shown by the following frequency distribution. Response ……………………………………………………………………………………. Frequency Good jobs ……………………………………………………………………
> In order to test if the population proportion differs from 0.40, you draw a random sample of 100 observations and obtain a sample proportion of 0.48. a. Specify the competing hypotheses. b. Is the normality condition satisfied? Explain. c. Calculate the
> The data accompanying this exercise show miles per gallon (MPG). a. State the null and the alternative hypotheses in order to test whether the average MPG differs from 95. b. Calculate the value of the test statistic and the p-value. c. At α = 0.05, can
> Construct the null and the alternative hypotheses for the following tests: a. Test if the mean weight of cereal in a cereal box differs from 18 ounces. b. Test if the stock price increases on more than 60% of the trading days. c. Test if Americans get an
> A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates a
> A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The manufacturer tested 12 of the cars and clocked their performance t
> Consider the following hypotheses: The population is normally distributed. A sample produces the following observations: Conduct the test at the 1% level of significance. H6 μ 2 100 На и < 100 95 99 85 80 98 97
> Consider the following hypotheses: The population is normally distributed. A sample produces the following observations: Conduct the test at the 5% level of significance. Ho: ju = 8 μ Hi fH # 8 A- 6 9 8 7 7 11 10
> Body mass index (BMI) is a reliable indicator of body fat for most children and teens. BMI is calculated from a child’s weight and height and is used as an easy-to-perform method of screening for weight categories that may lead to healt
> Consider the following hypotheses: a. A sample of 25 observations yields a sample mean of −12. Assume that the sample is drawn from a normal population with a sample standard deviation of 4. b. Calculate the value of the test statisti
> In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. Conduc
> In order to test if the population mean differs from 16, you draw a random sample of 32 observations and compute the sample mean and the sample standard deviation as 15.2 and 0.6, respectively. Conduct the test at the 1% level of significance.
> Consider the following hypotheses: A sample of 16 observations yields a sample mean of 46. Assume that the sample is drawn from a normal population with a sample standard deviation of 10. a. Calculate the value of the test statistic. b. At the 5% signi
> An economist wants to test if the average hourly wage is less than $22. Assume that the population standard deviation is $6. a. State the null and the alternative hypotheses for the test. b. The data accompanying this exercise show hourly wages. Find the
> The data accompanying this exercise show the weekly stock price for Home Depot. Assume that stock prices are normally distributed with a population standard deviation of $3. a. State the null and the alternative hypotheses in order to test whether or not
> According to the Centers for Disease Control and Prevention (February 18, 2016), 1 in 3 American adults don’t get enough sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a r
> A committee of 10 is to be chosen from 50 people, 25 of whom are Republicans and 25 Democrats. The committee is chosen at random. a. What is the probability that there will be five Republicans and five Democrats? b. What is the probability that a majorit
> Find the probability that an Internal Revenue Service (IRS) auditor will catch only 4 income tax returns with illegitimate deductions if he randomly selects 5 returns from among 20 returns, of which 10 contain illegitimate deductions.
> A professor has learned that three students in her class of 20 will cheat on the exam. She decides to focus her attention on four randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating? b
> Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had been involved in traffic accidents at the rate of 1,000 per
> Suppose you draw three cards, without replacement, from a deck of well-shuffled cards. Remember that each deck consists of 52 cards, with 13 each of spades, hearts, clubs, and diamonds. a. What is the probability that you draw all spades? b. What is the
> The police have estimated that there are 12 major accidents per day on a particular 10-mile stretch of a national highway. Suppose the incidence of accidents is evenly distributed on this 10-mile stretch of the highway. a. Find the probability that there
> Despite the fact that home prices seem affordable and mortgage rates are at historic lows, real estate agents say they are showing more homes, but not selling more (The Boston Globe, March 7, 2009). A real estate company estimates that an average of five
> Studies have shown that bats can consume an average of ten mosquitoes per minute (berkshiremuseum.org). a. Calculate the average number of mosquitoes that a bat consumes in a 30-second interval. b. What is the probability that a bat consumes four mosquit
> According to a survey by consulting firm Watson Wyatt, approximately 19% of employers have eliminated perks or plan to do so in the next year (Kiplinger’s Personal Finance, February 2009). Suppose 30 employers are randomly selected. a. What is the probab
> Twenty percent of U.S. mortgages are “underwater” (The Boston Globe, March 5, 2009). A mortgage is considered underwater if the value of the home is less than what is owed on the mortgage. Suppose 100 mortgage holders are randomly selected. a. What is th
> Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had been involved in traffic accidents at the rate of 1,000 per
> A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 4. a. What is the height of the density function f(x)? b. What are the mean and the standard deviation for the distribution? c. Calculate P(X ≤
> According to the Department of Transportation, 27% of domestic flights were delayed in 2007 (Money, May 2008). At New York’s John F. Kennedy Airport, five flights are randomly selected. a. What is the probability that all five flights are delayed? b. Wha
> Rent-to-own (RTO) stores allow consumers immediate access to merchandise in exchange for a series of weekly or monthly payments. The agreement is for a fixed time period. At the same time, the customer has the flexibility to terminate the contract by ret
> Discuss the factors that influence the margin of error for the confidence interval for the population mean. What can a practitioner do to reduce the margin of error?
> On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 15 minutes. a. Calculate the rate par
> A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour. a. What is the mean time between car arrivals at this tollbooth? b. What is the probability that the next car will arrive within ten seconds?
> An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. a. Calculate the expected value for the portfolio return. b. Calculate the standard deviation for the po
> A random variable X is exponentially distributed with a probability density function of f (x) = 5e−5x. Calculate the mean and the standard deviation of X.
> Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standa
> Facing the worst economic climate since the dot-com bust in the early 2000s, high-tech companies in the United States search for investment opportunities with cautious optimism (USA TODAY, February 17, 2009). Suppose the investment team at Microsoft is c
> An analyst developed the following probability distribution for the rate of return for a common stock. a. Calculate the expected rate of return. b. Calculate the variance and the standard deviation of this probability distribution. Scenario Probabi
> The car speeds on a certain stretch of the interstate highway I-95 are known to be normally distributed with a mean of 72 and a standard deviation of 15. You have just heard a policeman comment that about 3% of the drivers drive at extremely dangerous sp
> A random variable X follows the continuous uniform distribution with a lower bound of 5 and an upper bound of 35. a. What is the height of the density function f(x)? b. What are the mean and the standard deviation for the distribution? c. Calculate P(X >
> A committee of 40 members consists of 24 men and 16 women. A subcommittee consisting of 10 randomly selected members will be formed. a. What are the expected number of men and women on the subcommittee? b. What is the probability that at least half of th
> According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago (The New York Times, January 2, 2008). According to the New York City Youth Risk Be
> The National Science Foundation is fielding applications for grants to study climate change. Twenty universities apply for a grant, and only four of them will be awarded. If Syracuse University and Auburn University are among the 20 applicants, what is t
> David Barnes and his fiancée Valerie Shah are visiting Hawaii. There are 20 guests registered for orientation. It is announced that 12 randomly selected registered guests will receive a free lesson of Tahitian dance. a. What is the probability that both
> Many programming teams work independently at a large software company. The management has been putting pressure on these teams to finish a project on time. The company currently has 18 large programming projects, of which only 12 are likely to finish on
> Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the best years before the crisis (The Washington Post, January 1
> A professor of management has heard that eight students in his class of 40 have landed an internship for the summer. Suppose he runs into three of his students in the corridor. a. Find the probability that none of these students has landed an internship.
> Suppose you have an urn of ten marbles, of which five are red and five are green. If you draw two marbles from this urn, what is the probability that both marbles are red? What is the probability that at least one of the marbles is red?
> Compute the probability of at least eight successes in a random sample of 20 items obtained from a population of 100 items that contains 25 successes. What are the expected number and the standard deviation of the number of successes?
> Assume that X is a hypergeometric random variable with N = 50, S = 20, and n = 5. Calculate the following probabilities. a. P (X = 2) b. P (X ≥ 2) c. P (X ≤ 3)
> Compute the probability of no successes in a random sample of three items obtained from a population of 12 items that contains two successes. What are the expected number and the standard deviation of the number of successes from the sample?
> Assume that X is a hypergeometric random variable with N = 15, S = 4, and n = 3. Calculate the following probabilities. a. P (X = 1) b. P (X = 2) c. P (X ≥ 2)
> An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A report in The New York Times (November 23, 2009) suggests that 20.4% of laptops fail over three years. Roberto Dâ&
> A hospital administrator worries about the possible loss of electric power as a result of a power blackout. The hospital, of course, has a standby generator, but it, too, is subject to failure, having a mean time between failures of 500 hours. It is reas
> In the fiscal year that ended September 30, 2008, there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission, an increase of 29% from the previous year (The Wall Street Journal, March 7−8, 2009). Assume there were
> Due to the advent of tablets, American adults are watching significantly less television than they did in previous decades. In 2016, Nielsen reported that American adults are watching an average of five hours and four minutes, or 304 minutes, of televisi
> According to a government report, the aging of the U.S. population is translating into many more visits to doctors’ offices and hospitals (USA Today, August 7, 2008). It is estimated that an average person makes four visits a year to doctors’ offices and
