An associate dean of a university wishes to compare the means on the standardized final exams in microeconomics and macroeconomics. He has access to a random sample of 40 scores from each of these two courses. A portion of the data is shown in the accompanying table. Micro …………………………………………………………………………………………. Macro 85 …………………………………………………………………………………………………… 48 78 …………………………………………………………………………………………………… 79 ⋮ …………………………………………………………………………………………………………. ⋮ 75 ……………………………………………………………………………………………………. 74 a. Construct 95% confidence intervals for the mean score in microeconomics and the mean score in macroeconomics. b. Explain why the widths of the two intervals are different.
> The following table shows the annual returns (in percent) for the Vanguard Energy Fund. Year …………………………………………………………………………………………… Return 2010 …………………………………………………………………………………………………. 13 2011 …………………………………………………………………………………………………. −2 2012 ………………………………………………
> A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). Suppose this study was based on a random sample of 50 teen drivers. a. Construct the 99% confidence interval for the
> The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Ha
> Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall Street Journal, August 26, 2010). Let the rate of seriousl
> In a sample of 30 observations, the number of successes equals 18. a. Construct the 88% confidence interval for the population proportion of successes. b. Construct the 98% confidence interval for the population proportion of successes. c. What happens t
> Students who graduated from college in 2010 owed an average of $25,250 in student loans (The New York Times, November 2, 2011). An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their av
> Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 549, 449, 705, 529, 639, and 609. a. Construct the 95% confidence interval for the mean sale price in San Luis Obispo County. b. What ass
> According to data from the Organization for Economic Cooperation and Development, the average U.S. worker takes 16 days of vacation each year (The Wall Street Journal, June 20, 2007). Assume that these data were based on a sample of 225 workers and that
> A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. a.
> Over a 10-year sample period, the mean and the standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct the 95% confidence interval for the populatio
> A business student is interested in estimating the 99% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five per
> Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default
> On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Assume that game times are normally distributed with a standard deviation of 0.4
> Newscasters wish to estimate the proportion of registered voters who support the incumbent candidate in the mayoral election. In an earlier poll of 240 registered voters, 110 had supported the incumbent candidate. Find the sample size required to constru
> A budget airline wants to estimate what proportion of customers would consider paying $12 for in-flight wireless access. Given that the airline has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of err
> A random sample of 100 observations results in 40 successes. a. What is the point estimate for the population proportion of successes? b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that
> The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $18. The manager would like to construct the 95% confidence interval for the mea
> The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 16-inch pizzas. She takes a random sample of 25 pizzas and records their mean and standard deviation as 16.10 inches and 1.8 inches, respecti
> An analyst would like to construct 95% confidence intervals for the mean stock returns in two industries. Industry A is a high-risk industry with a known population standard deviation of 20.6%, whereas Industry B is a low-risk industry with a known popul
> An analyst from an energy research institute in California wishes to estimate the 99% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by mor
> Mortgage lenders often use FICO scores to check the credit worthiness of consumers applying for real estate loans. In general, FICO scores range from 300 to 850 with higher scores representing a better credit profile. A lender in a Midwestern town would
> You wish to compute the 95% confidence interval for the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.06? No prior estimate for the population
> 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
> Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 mpg and 3.5 mpg, respectively. a. What is the probability that a randomly selected passenger car gets
> A professional basketball team averages 80 points per game with a standard deviation of 10 points. Assume points per game follow the normal distribution. a. What is the probability that a game’s score is between 60 and 100 points? b. What is the probabil
> You need to compute the 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard devi
> A sample of 80 results in 30 successes. a. Calculate the point estimate for the population proportion of successes. b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that the population prop
> Find the required sample size for estimating the population mean in order to be 95% confident that the sample mean is within 10 units of the population mean. Assume that the population standard deviation is 40.
> At a local community college, 40% of students who enter the college as freshmen go on to graduate. Ten freshmen are randomly selected. a. What is the probability that none of them graduates from the local community college? b. What is the probability tha
> The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 16 minutes and 4 minutes, respectively. a. Find the probability that a randomly picked assembly takes between 10 and 20 minutes. b. It i
> Let X represent a binomial random variable with n = 200 and p = 0.77. Find the following probabilities. a. P (X ≤ 150) b. P (X > 160) c. P (155 ≤ X ≤ 165) d. P (X = 160)
> A survey conducted by CBS News asked 1,026 respondents: “What would you do with an unexpected tax refund?” The responses are summarized in the following table. Response ………………………………………………………………………………... Frequency Pay off debts ……………………………………………………………………
> An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% A’s, 23% B’s, 42% C’s, and 30% D’s and F’s. Assuming that this was a representative clas
> Let X represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities. a. P (X ≤ 50) b. P (X = 40) c. P (X > 60) d. P (X ≥ 55)
> In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.90, derive the interval estimate for the proportion of all homeo
> In an NBC News/Wall Street Journal poll of 1,000 American adults conducted August 5–9, 2010, 44% of respondents approved of the job that Barack Obama was doing in handling the economy. a. Compute the 90% confidence interval for the proportion of American
> The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. a. What percentage of rents are between $1,250 and $1,750? b. What percentage of rents are less than $1,250? c. What percentage
> Assume in a sample of size n = 50. a. Construct the 95% confidence interval for the population proportion. b. What happens to the margin of error if the above sample proportion is based on n = 200 instead of n = 50?
> Assume that IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 16. a. What is the probability that an individual scores between 84 and 116? b. What is the probability that an individual scores less than 68? c. What is t
> A survey of 1,026 people asked: “What would you do with an unexpected tax refund?” Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010). a. At 95% confidence, what is the margin of error? b. Construct the 95% confidence in
> According to a company’s website, the top 25% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and standard deviation of the test scores are 68 and 8, respectively
> Assume that X is a binomial random variable with n = 5 and p = 0.35. Calculate the following probabilities. a. P (X = 0) b. P (X = 1) c. P (X ≤ 1)
> The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds. b. Find the probability that a randomly selected turkey
> Americans are increasingly skimping on their sleep (National Geographic News, February 24, 2005). A health expert believes that American adults sleep an average of 6.2 hours on weekdays, with a standard deviation of 1.2 hours. Assume that sleep time on w
> The average high school teacher annual salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000. a. What percentage of high school teachers make between $40,000 and $50,000? b. Wha
> A portfolio has $200,000 invested in Asset X and $300,000 in Asset Y. Consider the summary measures in the following table. a. Calculate the portfolio weights for assets X and Y. b. Calculate the expected return for the portfolio. c. Calculate the stan
> Many of today’s leading companies, including Google, Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who believes that a university’s research expenditure (Research in $ million
> You own a portfolio that has $4,400 invested in stocks and $5,600 invested in bonds. What is the expected return of the portfolio if stocks and bonds are expected to yield a return of 9% and 5%, respectively?
> A random sample of 80 observations results in 50 successes. a. Construct the 95% confidence interval for the population proportion of successes. b. Construct the 95% confidence interval for the population proportion of failures.
> A study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The accompanying table shows a portion of average monthly debt payments (Debt in $) for 26 metropolitan areas. Construct 90% and 95% confiden
> What are the portfolio weights for a portfolio that has 100 shares of Stock X that sell for $20 per share and 200 shares of Stock Y that sell for $12 per share?
> A teacher wants to estimate the mean time (in minutes) that students take to go from one classroom to the next. His research assistant uses the sample time of 36 students to report the confidence interval as [8.20, 9.80]. a. Find the sample mean time use
> Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1690, 1810]. This confidence interval uses the sample mean and the sample standard deviation based on 25 observations. What are the sample mean a
> The historical returns on a balanced portfolio have had an average return of 8% and a standard deviation of 12%. Assume that returns on this portfolio follow a normal distribution. a. What percentage of returns were greater than 20%? b. What percentage o
> Let X be normally distributed with mean μ = 10 and standard deviation σ = 4. a. Find P (X ≤ 0). b. Find P (X > 2). c. Find P (4 ≤ X ≤ 10). d. Find P (6 ≤ X ≤ 14).
> A price-earnings ratio, or P/E ratio, is calculated as a firm’s share price compared to the income or profit earned by the firm per share. Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to
> As reported by tradingeconomics.com on September 2, 2012, the unemployment rates (in %) in major economies around the world were as follows: Country ……………………………………………………………………... Unemployment Rate Australia ……………………………………………………………………....................
> Let X be normally distributed with mean μ = 10 and standard deviation σ = 6. a. Find P (X ≤ 0). b. Find P (X > 2). c. Find P (4 ≤ X ≤ 10). d. Find P (6 ≤ X ≤ 14).
> The effort to reward city students for passing Advanced Placement tests is part of a growing trend nationally and internationally. Financial incentives are offered in order to lift attendance and achievement rates. One such program in Dallas, Texas, offe
> Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. a. Find P (X > 7.6). b. Find P (7.4 ≤ X ≤ 10.6). c. Find x such that P (X > x) = 0.025. d. Find x such that P (x ≤ X ≤ 2.5) = 0.4943.
> The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salari
> Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. a. Find P (X ≤ 86). b. Find P (80 ≤ X ≤ 100). c. Find x such that P (X ≤ x) = 0.40. d. Find x such that P (X > x) = 0.90.
> Mark Underwood is a professor of economics at Indiana University. He has been teaching Principles of Economics for over 25 years. Professor Underwood uses the following scale for grading. Grade ………………………………………………………………………………… Probability A …………………………………
> Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $25,000 on a clear day and $10,000 on a cloudy day. They will take a loss of $5,000 if it rains. The weath
> A random sample of eight drugstores shows the following prices (in $) of a popular pain reliever: Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean. 3.50 4.00 2.00 3.00 2.5
> Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. a. Calculate the sample mean and the sample standard deviation. b. Construct the 80% confidence interva
> An analyst has 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 Pro
> You were informed at the nursery that your peach tree will definitely bloom sometime between March 18 and March 30. Assume that the bloom times follow a continuous uniform distribution between these specified dates. a. What is the probability that the tr
> The Netherlands is one of the world leaders in the production and sale of tulips. Suppose the heights of the tulips in the greenhouse of Rotterdam’s Fantastic Flora follow a continuous uniform distribution with a lower bound of 7 inches and an upper boun
> For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing th
> Find tα, df from the following information. a. α = 0.025 and df = 12 b. α = 0.10 and df = 12 c. α = 0.025 and df = 25 d. α = 0.10 and df = 25
> A safety officer is concerned about speeds on a certain section of the New Jersey Turnpike. He records the speeds of 40 cars on a Saturday afternoon. The accompanying table shows a portion of the results. Assume that the population standard deviation is
> An economist wants to estimate the mean hourly wage (in $) of all workers. She collects data on 50 hourly wage earners. A portion of the data is shown in the accompanying table. Assume that the population standard deviation is $6. Construct and interpret
> After Donald Trump won the election, the consumer confidence index rose to 93.8, a six month high (www.bloomberg.com, November 23, 2016). Given new economic data, an analyst believes that there is a 75% chance that the index will fall below 90 and only a
> A manager is interested in estimating the mean time (in minutes) required to complete a job. His assistant uses a sample of 100 observations to report the confidence interval as [14.355, 17.645]. The population standard deviation is known to be equal to
> Suppose the 95% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$36,080, $43,920]. The population standard deviation used for the analysis is known to be $12,000. a. What is the point estimate of the me
> U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger’s, August 2007). Assume that this average was based on a sample of 100 consumers an
> A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the m
> A random variable X follows the continuous uniform distribution with a lower limit of 750 and an upper limit of 800. a. Calculate the mean and the standard deviation for the distribution. b. What is the probability that X is less than 770?
> A random variable X follows the continuous uniform distribution with a lower limit of 10 and an upper limit of 30. a. Calculate the mean and the standard deviation for the distribution. b. What is the probability that X is greater than 22? c. What is the
> Harvard University revolutionized its financial aid policies, aimed at easing the financial strain on middle and upper-middle income families (Newsweek, August 18–25, 2008). The expected contribution of students who are admitted to Harv
> The average life expectancy for Bostonians is 78.1 years (The Boston Globe, August 16, 2010). Assume that this average was based on a sample of 50 Bostonians and that the population standard deviation is 4.5 years. a. What is the point estimate of the po
> Identify the possible values of the following random variables. Which of the random variables are discrete? a. The numerical grade a student receives in a course. b. The grade point average of a student. c. The salary of an employee, defined in figures (
> Consider the following cumulative probability distribution. a. Calculate P (X ≤ 0). b. Calculate P (X = 50). c. Is this a discrete uniform distribution? Explain. X -25 25 50 P (X <x) 0.25 0.50 0.75 1
> An accounting professor wants to know the average GPA of the students enrolled in her class. She looks up information on Blackboard about the students enrolled in her class and computes the average GPA as 3.29. a. Describe the relevant population. b. Do
> Find Zα⁄2 for each of the following confidence levels used in estimating the population mean. a. 89% b. 92% c. 96%
> Find Zα⁄2 for each of the following confidence levels used in estimating the population mean. a. 90% b. 98% c. 88%
> Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco’s rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mea
> Consider the following hypothesis test: A random sample of 36 observations yields a sample mean of −125. The population standard deviation is 42. Conduct the test at α = 0.01. H μ=-100 H: μ+-100 –100
> Consider the following hypothesis test: A random sample of 100 observations yields a sample mean of 80. The population standard deviation is 30. Calculate the p-value. What is the conclusion to the test if α = 0.10? μ< 75 μ> 75 Hoi fe
> Consider the following hypothesis test: A random sample of 50 observations yields a sample mean of −3. The population standard deviation is 10. Calculate the p-value. What is the conclusion to the test if α = 0.05? H
> A researcher wants to determine if the population mean is greater than 45. A random sample of 36 observations yields a sample mean of 47. Assume that the population standard deviation is 8. a. Specify the competing hypotheses to test the researcher’s cla
> Consider the following hypotheses: a. A sample of 80 observations results in a sample mean of 144. The population standard deviation is known to be 28. b. Calculate the value of the test statistic and the p-value. c. Does the above sample evidence enab
> Consider the following hypotheses: A sample of 16 observations yields a sample mean of 95. Assume that the sample is drawn from a normal population with a population standard deviation of 10. a. Calculate the value of the test statistic. b. Find the p-
> American football is the highest paying sport on a pergame basis. Given that the quarterback is considered the most important player on an NFL team, he is typically well-compensated. Consider a portion of the following quarterback salary data (in $ milli
> Forty families gathered for a fund-raising event. Suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $115 and $35, respectively. The organizers would call this event a success if the total
> The typical college student graduates with $27,200 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $7,000. a. What is the probability that the average debt of four rec
> The following table shows the annual returns (in %) for two of Putnam’s mutual funds: the Voyager Growth Fund and the George Putnam Balanced Fund. a. Calculate and interpret the covariance. b. Calculate and interpret the correlation
> A manager of a local retail store analyzes the relationship between advertising (in $100s) and sales (in $1,000s) by reviewing the store’s data for the previous six months. Advertising ………………………………………………………………………………………… Sales 20 ………………………………………………………………
> The National Sporting Goods Association (NSGA) conducted a survey of the ages of individuals that purchased skateboarding footwear. The ages of this survey are summarized in the following percent frequency distribution. Age of User ………………………………………………………
