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business
business statistics communicating

Questions and Answers of Business Statistics Communicating

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
Consider the following sample regressions for the linear and the logarithmic models.a. Justify which model fits the data best.b. Use the selected model to predict y for x = 10. Linear Logarithmic
Consider the following sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2.a. Use the appropriate goodness-of-fit measure to justify which model fits
Consider the following sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2.a. Use the appropriate goodness-of-fit measure to justify which model fits
In a report, use the sample information to 1. Estimate and interpret CAPM: R − Rf = β0 + β1 (RM − Rf) + ε. Search for Apple’s reported Beta on the Web and compare it with your
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.
A financial analyst uses the following model to estimate a firm’s stock return: Return = β0 + β1P⁄E + β2P/S + ε, where P/E is a firm’s price-to-earnings ratio and P/S is a firm’s price-to
For a sample of 41 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). He
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
An analyst estimates the sales of a firm as a function of its advertising expenditures using the model: Sales = β0 + β1 Advertising + ε. Using 20 observations, he finds that SSR = 199.93 and SST =
The accompanying table lists goodness-of-fit measures that were obtained when estimating the following multiple linear regression models:Which model provides a better fit for y? Justify your response
The accompanying table lists goodness-of-fit measures that were obtained when estimating the following simple linear regression model and multiple linear regression model:Which model provides a
The accompanying table lists goodness-of-fit measures that were obtained when estimating the following simple linear regression model and multiple linear regression model:Which model provides a
The accompanying table lists goodness-of-fit measures that were obtained when estimating the following two simple linear regression models:Which model provides a better fit for y? Justify your
In a multiple regression with two explanatory variables, and 50 observations, it is found that SSE = 35 and SST = 90.a. Calculate the standard error of the estimate se.b. Calculate the coefficient of
In a simple linear regression based on 25 observations, it is found that SSE = 1,250 and SST = 1,500.a. Calculate s2e and se.b. Calculate R2.
The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008.a. Estimate the model:
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 value.b.
The covariance between two random variables x and y is −250. The sample standard deviation for x is 40 and the sample standard deviation for y is 50. Calculate and interpret the correlation
The covariance between two random variables x and y is 100. The sample standard deviation for x is 10 and the sample standard deviation for y is 12.5. Calculate and interpret the correlation
Suppose at the beginning of 2012 you decide to invest $20,000 in Driehaus’ Emerging Markets Growth mutual fund. The following table shows the returns (in %) for the years 2012–2016.Year . . . . .
The following table shows sales for Nike (in $ millions) for the years 2011 through 2015.a. Use the growth rates for 2011–2012, 2012–2013, 2013–2014, and 2014–2015 to calculate the average
The monthly closing stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. for the first six months of 2016 are reported in the following table.a. Calculate the sample
The accompanying table shows a portion of the annual return (in %) for the Fidelity Select Technology Fund and Fidelity Select Energy Fund from 2000 through 2016.a. Compare the sample means and the
Consider a sample with 10 observations of −3, 8, 4, 2, −4, 15, 6, 0, −4, and 5. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution.
The accompanying data file shows the annual return (in percent) for the Fidelity Select Technology Fund and the Fidelity Select Energy Fund from 2000 through 2016. Assume that the return data are
An environmentalist wants to examine whether average fuel consumption (measured in miles per gallon) is affected by fuel type (factor A) and type of hybrid (factor B). A two-way ANOVA experiment with
A data analyst for an online store wonders whether average customer visits to the store’s website vary by day of the week. He collects daily unique visits to the website for a 12-week period; a
The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.a. Calculate SST, SSA, SSB, and SSE.b. Calculate MSA, MSB, and MSE.c. Construct an ANOVA
A one-way analysis of variance experiment produced the following ANOVA table.a. Use Fisher’s LSD method to determine which means differ at the 5% level of significance.b. Use Tukey’s HSD method
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 (www.pewresearch.org, January 28, 2014). Due to this
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).
In a report, use the below information to 1. Describe the similarities and differences in these two funds’ returns.2. Examine whether the risk of one fund is different from the risk of the
Adidas revenues (in millions of €) in the Greater China and Western Europe regions for the years 2011 through 2015 are shown in the accompanying table. Assume revenues are normally distributed.a.
Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since
Consider the following competing hypotheses and relevant summary statistics:Conduct this hypothesis test at the 5% significance level. State your assumptions. Hoi oilo 1 Hai olo3
Consider the following competing hypotheses and relevant summary statistics:Conduct this test at the 5% significance level. State your assumptions. Họ: olo1 Sample 1: s = 935 and n, = 14 Sample 2:
Consider the following competing hypotheses and relevant summary statistics:Assume that the two populations are normally distributed. Conduct this test at the 5% significance level. Họ: olo = 1
Use the F table to find the following probabilities.a. P(F(10,8) ≥ 3.35)b. P(F(10,8) < 0.42)c. P(F(10,8) ≥ 4.30)d. P(F(10,8) < 0.26)
Use the F table to find the value x for which:a. P(F(4,8) ≥ x) = 0.025b. P(F(4,8) ≥ x) = 0.05c. P(F(4,8) < x) = 0.025d. P(F(4,8) < x) = 0.05
The data accompanying this exercise show miles per gallon (mpg) for 25 cars.a. State the null and the alternative hypotheses in order to test whether the variance differs from 62 mpg2.b. Assuming
A realtor in Mission Viejo, California, believes that the standard deviation of house prices is more than 100 units, where each unit equals $1,000. Assume house prices are normally distributed.a.
Consider the following hypotheses:Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population.a. s2 = 300; n = 25b. s2 = 100; n = 25c.
In order to conduct a hypothesis test for the population variance, you compute s2 = 75 from a sample of 21 observations drawn from a normally distributed population. Conduct the following tests at α
In order to construct a confidence interval for the population variance, a random sample of n observations is drawn from a normal population. Use this information to find and under
Fresh numbers from the U.S. Department of Transportation suggest that fewer flights in the United States arrive on time than before. The explanations offered for the lackluster performance are
A report suggests that business majors spend the least amount of time on course work than all other college students (The New York Times, November 17, 2011). A provost of a university decides to
A 2015 national survey by the Washington Post-Kaiser Family Foundation finds that there is a big gender divide between Americans when identifying as feminist or strong feminist. The results of the
There is a growing public support for marijuana law reform, with polls showing more than half the country is in favor of some form of marijuana legalization. However, opinions on marijuana are
According to eMarketer estimates, 88.3% of 12- to 17-year-olds had a mobile phone in 2016. Among those with mobile phones, 84.0% had smartphones. Calculate the proportion of 12-to 17-year-olds who
Let A and B be independent events with P(A) = 0.40 and P(B) = 0.50.a. Calculate P(A ∩ B).b. Calculate P((A ∪ B)c).c. Calculate P(A ∣ B).
Let P(A) = 0.55, P(B) = 0.30, and P(A ∩ B) = 0.10.a. Calculate P(A ∣ B).b. Calculate P(A ∪ B).c. Calculate P((A ∪ B)c).
Let P(A) = 0.65, P(B) = 0.30, and P(A ∣ B) = 0.45.a. Calculate P(A ∩ B).b. Calculate P(A ∪ B).c. Calculate P(B ∣ A).
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.
Consider the following sample data:a. Calculate the covariance.b. Calculate and interpret the correlation coefficient. 12 18 20 22 25 х 25 15 20 22 27 У
Consider the following sample data:a. Calculate the covariance.b. Calculate and interpret the correlation coefficient. -2 -2 -3 -8 -9 -10 y 4) 3.
The accompanying data file shows, among other variables, median household income and median house value for the 50 states in 2010. Assume that income and house value data are bell-shaped.a. Use
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). Let the standard deviation
Suppose at the beginning of 2012 you decide to invest $1,000 in Vanguard’s European Stock Index mutual fund. The following table shows the returns (in %) for the years 2012–2015.Year . . . . . .
In an effort to make children’s toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a
Consider the following competing hypotheses and accompanying sample data.a. Calculate the value of the test statistic.b. Find the p-value.c. At the 5% significance level, what is the conclusion to
Consider the following competing hypotheses and accompanying sample data.a. Calculate the value of the test statistic.b. Find the p-value.c. At the 5% significance level, what is the conclusion to
Consider the following competing hypotheses and accompanying sample data.a. Calculate the value of the test statistic.b. Find the p-value.c. At the 5% significance level, what is the conclusion to
A bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure that this is the case, the
A sample of 35 paired observations generates the following results: d̅ = 1.3 and sD = 3.8. a. Specify the appropriate hypotheses to test if the mean difference is greater than zero. b.
Consider the following competing hypotheses and accompanying sample data.Assume that the populations are normally distributed with equal variances.a. Calculate the value of the test statistic and the
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
Residents of Hawaii have the longest life expectancies in the United States, averaging 81.48 years (www.worldlifeexpectancy.com; data retrieved June 4, 2012). A sociologist collects data on the
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
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
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
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
Consider the following hypotheses: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.a.
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.
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
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
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
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.
In a report, use the above information to1. Calculate descriptive statistics to compare the returns of the mutual funds. 2. Assess reward by constructing and interpreting 95% confidence
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
The following table shows the annual returns (in percent) for Fidelity’s Electronics and Utilities funds.a. Derive the 99% confidence intervals for the mean returns for Fidelity’s Electronics and
The producer of a particular brand of soup claims that its sodium content is 50% less than that of its competitor. The food label states that the sodium content measures 410 milligrams per serving.
A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A
Fast bowling, also known as pace bowling, is an important component of the bowling attack in the sport of cricket. The objective is to bowl at a high speed and make the ball turn in the air and off
A production process is designed to fill boxes with an average of 14 ounces of cereal. The population of filling weights is normally distributed with a standard deviation of 2 ounces. Inspectors take
Major League Baseball Rule 1.09 states that “the baseball shall weigh not less than 5 or more than 5¼ ounces” (www.mlb.com). Use these values as the lower and the upper control limits,
A random sample of size n = 100 is taken from a population of size N = 2,500 with mean μ = −45 and variance σ2 = 81.a. Is it necessary to apply the finite population correction factor? Explain.
A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2.Calculate the expected value and the standard error for the sampling distribution of
In a report, use the sample information to1. Calculate and interpret the probability that temperature goes (a) below 2°C and (b) above 8°C using a normal distribution approximation.2. Calculate the
In 2015, the U.S. Census Bureau reported that the median income for American households was $52,353, whereas the mean income was $71,932 (www.census.gov, data retrieved March 26, 2017). Suppose

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