Question: A study conducted in September and October
A study conducted in September and October of 2010 found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again (The Wall Street Journal, November 29, 2010). Suppose the hiring intentions of the respondents were as follows: 
Six months later, a sample of 500 employers were asked their hiring intentions and gave the following responses 
a. Specify the competing hypotheses to test whether the proportions from the initial study have changed. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, what is the conclusion to the hypothesis test? Interpret your results.
Transcribed Image Text:
Definitely Hire Likely to Hire Hire Uncertain Will not Hire 37% 17% 28% 18% Definitely Hire Likely to Hire Hire Uncertain Will not Hire 170 100 120 110
> A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The accompanying table shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City Property Taxes
> Diversification is considered important in finance because it allows investors to reduce risk by investing in a variety of assets. It is especially effective when the correlation between the assets is low. Consider the accompanying table, which shows a p
> The new manager of a theater would like to offer discounts to increase the number of tickets sold for shows on Monday and Tuesday evenings. She uses a sample of 30 weeks to record the number of tickets sold on these two days. A portion of the data is sho
> In June 2009, an onslaught of miserable weather in New England played havoc with people’s plans and psyches. However, the dreary weather brought a quiet benefit to many city neighborhoods. Police reported that the weather was a key fact
> A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage in $), years of higher education (EDUC), years of experience (EXPER), and age (AGE). A portion of the data is shown in the
> 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 would like to analyze university factors that enhance
> There has been a lot of discussion regarding the relationship between Scholastic Aptitude Test (SAT) scores and test-takers’ family income (The New York Times, August 27, 2009). It is generally believed that the wealthier a student&acir
> A research analyst is trying to determine whether a firm’s price earnings (P/E) and price-sales (P/S) ratios can explain the firm’s stock performance over the past year. A P/E ratio is calculated as a firm’s share price compared to th
> The homeownership rate in the U.S. was 67.4% in 2009. In order to determine if homeownership is linked with income, 2009 state-level data on the homeownership rate (Ownership in %) and median household income (Income in $) were collected. A portion of th
> In response to the Great Recession, Federal Reserve leaders continue to keep the short-run target interest rate near zero. While the Fed controls short-term interest rates, long-term interest rates essentially depend on supply and demand dynamics, as wel
> A sample of 25 observations provides the following statistics: a. Calculate and interpret the sample correlation coefficient rxy. b. Specify the competing hypotheses in order to determine whether the population correlation coefficient differs from zer
> The following table shows a portion of the monthly returns data (in percent) for 2010–2016 for two of Vanguard’s mutual funds: The Vanguard Energy Fund and the Vanguard Healthcare Fund. a. Calculate and interpret the
> Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win in %), the average number of yards gained, and the average number of yards allowed during the 2009 NF
> Consider the following information on the expected return for companies X and Y. a. Calculate the expected value and the standard deviation of returns for companies X and Y. b. Calculate the correlation coefficient if the covariance between X and Y is
> The accompanying data file shows the selling price of a used sedan, its age, and its mileage. Estimate two models: Which model provides a better fit for y? Justify your response with two goodness-of-fit measures. Model 1: Price =Bo+BjX¡Age + E Mode
> The accompanying data file shows the square footage and associated property taxes for 20 homes in an affluent suburb 30 miles outside New York City. a. Estimate a home’s property taxes as a linear function of the size of the home (measured by its square
> The director of college admissions at a local university is trying to determine whether a student’s high school GPA or SAT score is a better predictor of the student’s subsequent college GPA. She formulates two models:
> A sample of 10 observations provides the following statistics: a. Calculate and interpret the sample correlation coefficient rxy. b. Specify the competing hypotheses to determine whether the population correlation coefficient is positive. c. Calculate
> The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans. a. Estimate the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage.
> The accompanying table shows a portion of data consisting of the rent, the number of bedrooms, the number of bathrooms, and the square footage for 40 apartments in the college town of Ann Arbor, Michigan a. Determine the sample regression equation that
> Consider the following competing hypotheses: The sample consists of 30 observations and the sample correlation coefficient is −0.60. a. Calculate the value of the test statistic and the p-value. b. At the 5% significance level, what
> American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression mode
> The facility manager at a pharmaceutical company wants to build a regression model to forecast monthly electricity cost. Three main variables are thought to dictate electricity cost (in $): (1) average outdoor temperature (Avg Temp in °F), (2)
> Education reform is one of the most hotly debated subjects on both state and national policy makers’ list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student perf
> Calculate the expected numerical grade in Professor Underwood’s class using 4.0 for A, 3.0 for B, etc.
> The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in
> A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home (Price in $), its square footage (Sqft), the number of bedrooms (Beds), and the number of bathrooms (Baths). She collects data on 36 sales in Arlington
> Finger dexterity, the ability to make precisely coordinated finger movements to grasp or assemble very small objects, is important in jewelry making. Thus, the manufacturing manager at Gemco, a manufacturer of high-quality watches, wants to develop a reg
> A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights
> Refer to the accompanying data file on happiness and age to answer the following questions. a. Estimate a simple linear regression model with Happiness as the response variable and Age as the explanatory variable. b. Use the sample regression equation t
> Consider the following competing hypotheses: The sample consists of 25 observations and the sample correlation coefficient is 0.15. a. Calculate the value of the test statistic and the p-value. b. At the 5% significance level, what is the conclusion
> A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary ………………………………………………………
> Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of Strong Bones, a prescription drug for treating this debilitating disease. She uses the model Sales = β0 + &I
> A sociologist believes that the crime rate in an area is significantly influenced by the area’s poverty rate and median income. Specifically, she hypothesizes crime will increase with poverty and decrease with income. She collects data
> Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of hig
> A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 5% chance that it will not make any hires and a 10% chance that it
> On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that p
> The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car’s age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Î&sup
> If a firm spends more on advertising, is it likely to increase sales? Data on annual sales (in $100,000s) and advertising expenditures (in $10,000s) were collected for 20 firms in order to estimate the model Sales = β0 + β1Adverti
> Forty observations were used to estimate y = β0 + β1x1 + β2x2 + ε. A portion of the regression results is shown in the accompanying table. a. What is the estimate for β1? Interpret this value
> Thirty observations were used to estimate y = β0 + β1x1 + β2x2 + ε. A portion of the regression results is shown in the accompanying table. a. What is the estimate for β1? Interpret this valu
> Twenty-four observations were used to estimate y = β0 + β1x + ε. A portion of the regression results is shown in the accompanying table. a. What is the estimate for β1? Interpret this value. b. What is
> The following table lists the National Basketball Association’s leading scorers, their average points per game (PPG), and their average minutes per game (MPG) for 2008. a. Calculate and interpret the sample correlation coefficient be
> Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). Th
> In 2003, The World Wealth Report first started publishing market shares of global millionaires (The Wall Street Journal, June 25, 2008). At this time, the distribution of the world’s people worth $1 million or more was as follows Region …………………………………………
> Despite Zimbabwe’s shattered economy, with endemic poverty and widespread political strife and repression, thousands of people from overseas still head there every year (BBC News, August 27, 2008). Main attractions include the magnificent Victoria Falls,
> Powerball is a jackpot game with a grand prize starting at $20 million and often rolling over into the hundreds of millions. In 2006, the jackpot was $365 million. The winner may choose to receive the jackpot prize paid over 29 years or as a lump-sum pay
> Go to www.zillow.com/ and find the sale price data of 20 single-family homes sold in Las Vegas, Nevada, in the last 30 days. In the data set, include the sale price, the number of bedrooms, the square footage, and the age of the house. What type of data
> A rent-to-own (RTO) agreement appeals to low-income and financially distressed consumers. It allows immediate access to merchandise, and by making all payments, the consumer acquires the merchandise. At the same time, goods can be returned at any point w
> The value of a college degree is greater than it has been in nearly half a century, at least when compared to the prospect of not getting a degree Due to this fact, more and more people are obtaining college degrees, despite the soaring costs. The accomp
> Reorder point decisions for a particular part at an automotive parts distributor are based on the assumption that weekly demand is normally distributed. (Note: “Reorder point” is the inventory level at which a replenishment order is placed; it should be
> You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following frequencies: a. Specify the null and alternative hypothes
> A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability distributions. The software design group would like to validate tha
> The human resources department would like to consolidate the current set of retirement plan options offered to specific employee pay groups into a single plan for all pay groups (salaried, hourly, or piecework). A sample of 585 employees of various pay g
> The operations manager at Electro Tech, an electronics manufacturing company, believes that workers on particular shifts may be more likely to phone in “sick” than those on other shifts. To test this belief, she has co
> Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose “green” status indicates that an assembly line is operating normally, “yellow” indicates it is down waiting on p
> An automotive parts company has been besieged with poor publicity over the past few years due to several highly publicized product recalls that have tarnished its public image. This has prompted a series of quality improvement initiatives. Currently, the
> The number of homes that a realtor sells over a one-month period has the following probability distribution. Number of Houses Sold ……………………………………………………. Probability 0 ……………………………………………………………………………………………… 0.30 1 ……………………………………………………………………………………………… 0.50
> The data that accompany this exercise show various variables, including price and square footage, for 36 single-family homes in Arlington, Massachusetts, sold in the first quarter of 2009. a. Use the Jarque-Bera test to test if house prices are not norm
> The following frequency distribution shows the monthly stock returns (in percent) for Home Depot for the years 2003 through 2007. Monthly Returns ……………&a
> Given a shaky economy and high heating costs, more and more households are struggling to pay utility bills (The Wall Street Journal, February 14, 2008). Particularly hard hit are households with homes heated with propane or heating oil. Many of these hou
> A poll asked 3,228 Americans aged 16 to 21 whether they are likely to serve in the U.S. military. The following table, cross-classified by a person’s sex and race, reports those who responded that are likely or very likely to serve in t
> An analysis of variance experiment produced a portion of the following ANOVA table. Source of Variation a. Specify the competing hypotheses in order to determine whether some differences exist between the population means. b. Fill in the missing statis
> An analysis of variance experiment produced a portion of the accompanying ANOVA table. a. Specify the competing hypotheses in order to determine whether some differences exist between the population means. b. Fill in the missing statistics in the ANOVA
> Consider the following regression results based on 20 observations. a. Specify the hypotheses to determine if the intercept differs from zero. Perform this test at the 5% significance level. b. Construct the 95% confidence interval for the slope coeffi
> Mechanics In a simple linear regression based on 30 observations, it is found that b1 = 3.25 and se (b1) = 1.36. Consider the hypotheses: a. Calculate the value of the test statistic. b. Find the p-value. c. At the 5% significance level, what is the c
> Random sampling from four normally distributed populations produced the following data: a. Calculate the grand mean. b. Calculate SSTR and MSTR. c. Calculate SSE and MSE. d. Specify the competing hypotheses in order to determine whether some differen
> Mechanics A random sample of five observations from three normally distributed populations produced the following data: a. Calculate the grand mean. b.Calculate SSTR and MSTR. c. Calculate SSE and MSE. d.Specify the competing hypotheses in order to d
> Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none. a. What is the probability that a customer buys three tires? b. Construct a cumulative
> Akiko Hamaguchi is a manager at a small sushi restaurant in Phoenix, Arizona. Akiko is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. In order to offset the decline in sales,
> In the carbonated beverage industry, dispensing pressure can be an important factor in achieving accurate fill volumes. Too little pressure can slow down the dispensing process. Too much pressure can create excess “fizzâ€
> Wenton Powersports produces dune buggies. They have three assembly lines, “Razor,” “Blazer,” and “Tracer,” named after the particular dune buggy m
> For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the accom
> In a simple linear regression based on 25 observations, it is found that b1 = 0.5 and se(b1) = 0.3. Consider the hypotheses: a. Calculate the value of the test statistic and the p-value. b. At the 5% significance level, what is the conclusion to the t
> A study on the evolution of mankind shows that, with a few exceptions, world-record holders in the 100-meter dash have progressively gotten bigger over time (The Wall Street Journal, July 22, 2009). The following table shows runners who have held the rec
> A survey by Genworth Financial Inc., a financial-services company, concludes that the cost of long-term care in the United States varies significantly, depending on where an individual lives (The Wall Street Journal, May 16, 2009). An economist collects
> A well-known conglomerate claims that its detergent “whitens and brightens better than all the rest.” In order to compare the cleansing action of the top three brands of detergents, 24 swatches of white cloth were soi
> Applications Asian residents in Boston have the highest average life expectancy of any racial or ethnic group—a decade longer than black residents (The Boston Globe, August 16, 2010). Suppose sample results indicative of the overall res
> In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates Price = β0 + β1Age + ε. A portion of the regression results is s
> A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pound. a. I
> Applications A marketing manager analyzes the relationship between the annual sales of a firm (in $100,000s) and its advertising expenditures (in $10,000s). He collects data from 20 firms and estimates Sales = β0 + β1Advertising +
> The following ANOVA table was obtained when estimating a multiple linear regression model. a. How many explanatory variables were specified in the model? How many observations were used? b. Specify the hypotheses to determine whether the explanatory v
> A researcher examines the factors that influence student performance. She gathers data on 224 school districts in Massachusetts. The response variable is the students’ mean score on a standardized test (Score). She uses four explanatory
> Consider a regression model for per capita income, y. The explanatory variables consist of the percentage of the population in the U.S. that is (a) without a high school diploma, x1, (b) foreign born, x2, and (c) non-English speaking, x3. A portion of th
> A nutritionist wants to understand the influence of income and healthy food on the incidence of smoking. He collects 2009 data on the percentage of smokers in each state in the U.S. and the corresponding median income (in $) and the percentage of the pop
> A research analyst is trying to determine whether a firm’s priceearnings (P⁄E) and price-sales (P⁄S) ratios can explain the firm’s stock performance over the past year. Generally, a
> A government researcher examines the factors that influence a city’s crime rate. For 41 cities, she collects the crime rate (crimes per 100,000 residents), the poverty rate (in %), the median income (in $1,000s), the percent of resident
> George believes that the returns of mutual funds are influenced by annual turnover rates and annual expense ratios. In order to substantiate his claim, he randomly selects 20 mutual funds and collects data on each fund’s five-year annua
> A researcher studies the relationship between SAT scores, the test-taker’s family income (Income), and his/her grade point average (GPA). Data are collected from 24 students. A portion of the data is shown in the accompanying table. a
> The home ownership rate in the U.S. was 67.4% in 2009. In order to determine if home ownership is linked with income, 2009 state-level data on the home ownership rate (Ownership in %) and median household income (Income in $) were collected. A portion of
> A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $72,000 with a standard deviation of $3,000. a. Using Chebyshev’s theorem, what percentage of the faculty earns at least $66,000 but
> When estimating a multiple linear regression model based on 30 observations, the following results were obtained. // a. Specify the hypotheses to determine whether x1 is linearly related to y. At the 5% significance level, are x1 and y linearly related
> A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. Estimate: Happiness = β0 + β1Age + ε. At the 1% significance level, is Age s
> The labor estimation group at Sturdy Electronics, a contract electronics manufacturer of printed circuit boards, wants to simplify the process it uses to quote production costs to potential customers. They have identified the primary drivers for producti
> The consumption function is one of the key relationships in economics, where consumption y depends on disposable income x. Consider the quarterly data for these seasonally adjusted variables, measured in billions of dollars. A portion of the data is show
> Healthy living has always been an important goal for any society. In an ad campaign for Walt Disney, former First Lady Michelle Obama shows parents and children that eating well and exercising can also be fun (USA Today, September 30, 2010). Consider a r
> Consider the monthly rent (Rent in $) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft). a. Estimate: Rent = β0 + β1Beds + β2Baths + β3Sqft + ε. b. Which of the e
> Consider the following regression results based on 40 observations. a. Specify the hypotheses to determine if the slope differs from minus one. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, does the s
> Quick2U, a delivery company, would like to standardize its delivery charge model for shipments (Charge in $) such that customers will better understand their delivery costs. Three explanatory variables are used: (1) distance (in miles), (2) shipment weig
> A simple linear regression, y = β0 + β1x + ε, is estimated with time series data. The resulting residuals e and the time variable t are shown in the accompanying table. a. Graph the residuals against time and look f
