Questions and Answers of Business Statistics Communicating

Consider the following adjusted closing stock prices of a company. Find the monthly returns for January and February of 2020. Date January 1, 2020 February 1, 2020 March 1, 2020 Adjusted Closing
JJ Diner is a small mom and pop restaurant in a small town. They offer three choices for breakfast: omelets, pancakes, or cereal. The average prices (in $) for these options for 2017, 2018, and 2019
The accompanying table shows the number of SaaS subscriptions for each type of usage for 2018, 2019, and 2020 described in the previous exercise. Use this information, along with the price data
A software company offers several pricing options for its software as a service (SaaS) product. SaaS is a software licensing and delivery model in which software is licensed on a subscription basis
The accompanying table shows a portion of the price data from 2012 to 2020. a. Compute the simple price index using 2012 as the base year.b. Determine the percentage change in prices from 2012 to
A private college in Wisconsin offers an MBA program for executives. The following table shows the tuition for the program from 2014 to 2019. a. Use 2014 as the base year to form a simple price
Consider the following adjusted closing stock prices for two software development firms. Compute and compare the monthly returns for both firms from January 2020 to May 2020.
Consider the following price and quantity data for three products from 2018 to 2020.a. Compute the simple price index for each product, using 2018 as the base year.b. Compare the relative price
The following table shows the monthly adjusted closing price per share of a manufacturing firm from October 2019 to March 2020. a. Form a simple price index with October 2019 as the base period. b.
Consider the following price data from 2018 to 2020. a. Compute and interpret the simple price index for each product, using 2018 as the base year.b. Compute and interpret the unweighted aggregate
The accompanying table shows the consumer price index for China, India, and the U.S. for 2018 and 2019, each using the base period of 2015. Compute the inflation rate for each country in 2019.
Amy Lin’s condominium that she bought in 2016 for $240,000 has gone up in value to $250,000 in 2019.a. What is the percentage price change of Amy’s condominium from 2016 to 2019?b. What is the
The revenue of a software development firm grew from $10 million in 2000 to $22 million in 2019. a. What is the percentage price change of revenue from 2000 to 2019?b. What is the corresponding
In January 2020, you bought 100 shares of Tesla stock for $65,057. In May 2020, the value of your investment increased to $83,500. a. Find the nominal percentage price increase of your
The accompanying data file shows the growth rate in the gross domestic product (GDP) for India from 1990 through 2018. Use the method of runs above and below the median with a significance level of
The accompanying data file shows the gross domestic product (GDP) for China from 1990 through 2018. Use the method of runs above and below the median with a significance level of 5% to test the null
The accompanying data file has the monthly returns (in %) for Apple over a five-year period. Estimate the capital asset pricing model (CAPM) for Apple where the risk-adjusted stock return (Apple_Adj)
The accompanying data file shows information on 264 initial public offering (IPO) firms. The data include the initial return (Initial), price revision (Revision), and whether or not the firm is
An analyst for a mortgage company wants to better understand the quantitative relationship between housing starts (in 1,000s), the mortgage rate (in %), and the unemployment rate (in%). She gathers
The accompanying file contains data for y. a. Estimate an autoregressive model of order 1, yt = β0 + β1yt−1 + εt, to make a one-step-ahead forecast (t = 25) for y. b. Estimate an
Consider the following trend models estimated from 30 observations.Linear Model: ŷ = 24 + 0.12t Quadratic Model 2: ŷ = 30 + 0.20t − 0.01t2a. Use each model to make a forecast for y at t = 31
You collect the following sample data concerning average life expectancies for female and male residents in Boston. You assume a population standard deviation of 8.2 years for females and 8.6 years
The following table lists the market shares of the four firms in a particular industry in 2019 and total sales (in $ billions) for each firm in 2020.a. Specify the competing hypotheses to test
While the frequency of online shopping is lower for men as compared to women, men are the big spenders when it comes to making costly online purchase. A manager at the online retail store has
The accompanying data file contains the annual stock return (in %), the price-to-earnings ratio (PE), and the price-to-sales ratio (PS) for 30 firms.a. Estimate the model: Return = β0 + β1PE +
A consumer advocate in California is concerned with the price of a common generic drug. Specifically, he feels that one region of the state has significantly different prices for the drug than two
A sociologist studies the relationship between weather and crime in a city. Specifically, she believes that dreary weather is a key factor in reducing fatal and nondeadly shootings. She collects data
The average life expectancy for residents of Hawaii is 81.48 years (travelandleisure.com, July 16, 2018). A sociologist collects data on the age at death for 50 recently deceased Michigan
According to a survey, half of U.S. households have no emergency savings (The Wall Street Journal, April 16, 2020). An analyst in the Midwest collects data on 200 households and finds that 84 of them
According to a survey, 44% of adults admit to keeping money secrets from a partner (cnbc.com, February 20, 2020). Suppose this survey was based on 1,000 respondents. a. Compute the 90%
Many U.S. consumers are using debit cards to avoid accruing debt (creditkarma.com, July 27, 2019). Based on a sample of 100 U.S. consumers, a researcher finds that the average amount spent annually
Residents of Hawaii have the longest life expectancies, averaging 81.3 years (travelandleisure.com, July 16, 2018). A sociologist collects data on the age at death for 50 recently deceased Michigan
A study found that 55% of British firms experienced a cyberattack in the past year (bbc.com, April 23, 2019). Suppose that the study was based on 600 British firms. a. At 95% confidence, what is
A study finds that students who graduated from college in 2015 owed an average of $25,250 in student loans. An economist wants to determine if average debt has changed. She takes a sample of 40
A study reports that recent college graduates from Connecticut face the highest average debt of $38,510 (forbes.com, September 18, 2019). A researcher from Pennsylvania wants to determine how recent
The California Highway Patrol (CHP) routinely compiles car crash data in California. The accompanying table shows a portion of the data for Santa Clara county. It shows information on the type of car
There have been numerous attempts that relate happiness with income. In a recent survey, 290 individuals were asked to evaluate happiness (Yes or No) and income (Low, Medium, or High). The
Complete the following probability table. Prior Probability P(B) = 0.85 P(Bº) == Total = Conditional Probability P(AIB) = 0.05 P(AIB) = 0.80 Joint Probability P(An B) = P(An B) = P(A)
The subscription e-commerce market has grown substantially including subscription boxes that provide a recurring delivery of niche products. E-commerce firms pay attention to the churn rate defined
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%,
A study finds that approximately 43% of millennials are not investing in stocks, bonds, real estate and more. This is a problem because people who start investing when they are first starting their
A recent survey found that 82% of college graduates believe their degree was a good investment (cnbc.com, February 27, 2020). Suppose a random sample of 100 college graduates is taken.a. What is the
In general, normal blood pressure readings are those below 120/80 millimeters of mercury (www. mayoclinic.org, January 9, 2019). Prehypertension is suspected when the top number (systolic) is between
According to new research, 26% of Americans are (almost) always online (bigthink.com, March 20, 2018). a. What is the probability that fewer than 60 of 200 Americans are always online?b. What is
One-fifth of Britains are not using the internet (bbc.com, September 9, 2019).a. What is the expected value and the standard error for the sampling distribution of the sample proportion based on a
A health expert evaluates the sleeping patterns of adults. Each week she randomly selects 40 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time
AirPods are Apple’s most popular accessory product, with 35 million units sold in 2018 alone (AppleInsider, March 15, 2019). Suppose you are put in charge of determining the age profile of people
Georgia residents spend an average of $470.73 on the lottery, or one percent of their personal income (investopedia.com, June 25, 2019). Suppose the amount spent on the lottery follows a normal
American workers are increasingly planning to delay retirement (cnbc.com, Aug 25, 2019). A researcher finds that 35% of employed adults of age 62 and older say they have pushed back their retirement
Using 5,000 observations, the following histogram summarizes Variable X.a. Is the distribution symmetric? If not, is it positively or negatively skewed? b. What proportion of the observations are
The following table shows the revenues (in $ millions) for Firm 1 and Firm 2 over the past three years.a. Calculate the average growth rate for each firm. b. Which firm had the higher growth rate
The following table lists a portion of the average price (in $) for a gallon of gas for the 50 states and the District of Columbia as reported by AAA Gas Prices on January 28, 2020.a. Construct the
The accompanying table lists a portion of the ages and net worth of the 25 wealthiest people in the United States in 2019.RankNameAgeNet Worth1Jeff Bezos56131.02Bill Gates6496.53Warren
Using 3,000 observations, the following histogram summarizes Variable X.a. Is the distribution symmetric? If not, is it positively or negatively skewed? b. What proportion of the observations are
A statistics instructor is interested in the class status of her students, which is defined as freshman, sophomore, junior, or senior. She downloads her roster, a portion of which is shown in the
Using 1,000 observations, the following ogive summarizes Variable X. a. Approximate the proportion of observations that are less than 16. b. Approximate the number of observations that are greater
France was the winner of the FIFA 2018 World Cup, beating Croatia by a score of 4-2. The accompanying data file shows the ages of the players from both teams. Construct a stem-and-leaf diagram for
The following contingency table shows shipments received by a large firm. The shipments have been cross-classified by Vendor (I, II, and III) and Quality (Defective and Acceptable).a. How many
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
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 =
In an attempt to determine whether or not a linear relationship exists between the price of a home (in $1,000s) and the number of days it takes to sell the home, a real estate agent collected data
GPA = β0 + β1 GRE + ε, where GRE is a student’s score on the math portion of the Graduate Record Examination (GRE) score and GPA is the student’s grade point average in graduate school.a.
Estimate: Height = β0 + β1 Fertilizer + ε, where Height is a tomato plant’s height (in inches) and Fertilizer is the fertilizer amount (in ounces). a. Calculate and interpret the 90%
In a multiple linear regression based on eight observations, the following sample regression is obtained: ŷ = 22.81 + 0.85x1 - 0.71x2 with se = 4.69. Also, when x1 equals 50 and x2 equals 20,
In a simple linear regression based on eight observations, the following sample regression is obtained: ŷ = 9.15 + 1.46x with se = 2.67. Also, when x equals 15, se(ŷ0) = 1.06.a. Construct the 95%
Consider the multiple linear regression model, y = β0 + β1x1 + β2x2 + ε. Define the restricted and unrestricted models if the hypotheses are Họ: Bị + B2 = 1 and Ha: B + B2 +1
Consider the multiple linear regression model, y = β0 + β1x1 + β2x2 + β3x3 + ε. You wish to test whether the slope coefficients β1 and β3 are statistically different from each other. Define
Consider the multiple linear regression model, y = β0 + β1x1 + β2x2 + β3x3 + ε. You wish to test whether the slope coefficients β1 and β3 are jointly significant. Define the restricted and
In a report, use the sample information to1. Estimate and interpret the model: Consumption = β0 + β1 Disposable Income + ε.2. Indicate which assumption might be violated, given that the analysis
In a report, use the sample information to1. Calculate and interpret relevant summary measures for California home prices in these two regions.2. Explain why the t test for comparing means from
The following data are provided for two samples drawn from independent populations: W = 700, n1 = 25, and n2 = 20. Suppose the distribution of W is approximately normal.a. Calculate the mean and the
A matched-pairs sample of 20 observations produced a test statistic of T = 165.a. Specify the competing hypotheses in order to determine whether the median difference is greater than zero.b.
A realtor in Mission Viejo, California, believes that the median price of a house is more than $500,000. The accompanying data is in $1,000s.a. Specify the competing hypotheses for the test.b. At the
The following table lists a portion of the data representing the annual returns (in percent) over a 10-year period for the Balanced mutual fund, a top-performing mutual fund from the Janus Capital
Consider the following sample data:a. Specify the competing hypotheses to determine whether the median is greater than 140.b. Calculate the value of the test statistic T.c. The p-value corresponding
Consider the following sample data:a. Specify the competing hypotheses to determine whether the median differs from 20. b. Calculate the value of the test statistic T.c. The p-value
Consider the following adjusted closing stock prices for Ford Motor Company (Ford) and General Motors Company (GM). Compute and compare the monthly returns for both companies from January 2017 to May
Consider the following adjusted closing stock prices for Intel Corporation. Find the monthly returns for January and February of 2017. Adjusted Closing Price Date January 1, 2017 February 1, 2017
You borrowed $2,000 to take a vacation in the Caribbean islands. At the end of the year, you had to pay back $2,200. What is the annual interest that you paid on your loan?
Tourism was hit hard by the international financial crisis that began in the fall of 2008. According to the Bureau of Economic Analysis (December 20, 2010), tourism spending has picked up, but it
The following table lists a portion of the University of Michigan’s Consumer Sentiment Index. This index is normalized to have a value of 100 in 1965 and is used to record changes in consumer
Refer to the previous exercise for a description of the data set. a. Estimate a linear trend model with seasonal dummy variables. b. Estimate a quadratic trend model with seasonal dummy
Refer to the previous exercise for a description of the data set. Estimate a linear trend model with seasonal dummy variables to make forecasts for the first three months of 2011.Data from previous
The accompanying data file contains monthly observations for 5 years.a. Construct the seasonal indices for the data.b. Plot the seasonally adjusted series to recommend the appropriate trend model.c.
The accompanying data file contains quarterly observations for 5 years.a. Plot the series and discuss its trend and seasonal components.b. Use decomposition analysis to make in-sample forecasts with
The accompanying data file contains monthly observations for 5 years. Calculate and interpret the seasonal indices for April and November.
The accompanying data file contains quarterly observations for 5 years. Calculate and interpret the seasonal indices for quarters 1 and 4.
Ten years of monthly data of a seasonally adjusted series are used to estimate a linear trend model as T̂t = 24.50 + 0.48t. In addition, seasonal indices for January and February are calculated as
Eight years of quarterly data of a seasonally adjusted series are used to estimate an exponential trend model as with a standard error of the estimate, se = 0.08. In addition, quarterly
Six years of quarterly data of a seasonally adjusted series are used to estimate a linear trend model as T̂t = 128.20 + 1.06t. In addition, quarterly seasonal indices are calculated as Ŝ1 = 0.93,
Apple Inc. has performed extremely well in the last decade. After its stock price dropping to below 90 in May 2016, it made a tremendous come back to reach about 146 by May 2017 (SeekingAlpha.com,
With a new chef and a creative menu, Café Venetian has witnessed a huge surge in sales. The following data show a portion of daily sales (in $) at Café Venetian in the first 100 days after the
The number of cars sold in the United States in 2016 reached a record high for the seventh year in a row (CNNMoney, January 4, 2017). Consider monthly total miles traveled (in billions) in the United
Investors are always reviewing past pricing history and using it to influence their future investment decisions. On May 16, 2014, online car buying system TrueCar launched its initial public offering
Refer to the previous exercise for a description of the data set. Estimate the logit model where the Under Armour purchase depends on age.a. Compute the predicted probability of an Under Armour
House price y is estimated as a function of the square footage of a house x; a dummy variable d that equals 1 if the house has ocean views and 0 otherwise; and the interaction variable xd. The
Use the accompanying data to estimate a linear regression model with Math as the response variable and GPA and Female as the explanatory variables. a. Compute the predicted math score for a male
Using 50 observations, the following regression output is obtained from estimating y = β0 + β1x + β2d1 + β3d2 + ε.a. Compute ŷ for x = 250, d1 = 1, and d2 = 0; compute for x = 250, d1 = 0, and
Professor Orley Ashenfelter of Princeton University is a pioneer in the field of wine economics. He claims that, contrary to old orthodoxy, the quality of wine can be explained mostly in terms of
Consider the following sample regressions for the log-log and the exponential models.a. Justify which model fits the data best.b. Use the selected model to predict y for x = 20. Log-Log Exponential

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