Statistical Methods for Business Exam Preparation Guide
Course Introduction
Statistical Methods for Business introduces students to the fundamental statistical concepts and techniques widely used in business decision-making. The course covers descriptive statistics, probability distributions, sampling methods, hypothesis testing, confidence intervals, correlation, and regression analysis. Emphasis is placed on applying statistical tools to real-world business problems, interpreting data, and drawing informed conclusions. By the end of the course, students will be equipped to analyze data critically and make evidence-based decisions in a business context.
Recommended Textbook
Business Statistics Communicating with Numbers 3rd Edition by Sanjiv Jaggia
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Page 2
Chapter 1: Statistics and Data
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Sample Questions
Q1) Which of the following variables is quantitative?
A) Gender
B) Temperature
C) Marital status
D) Religious affiliation
Answer: B
Q2) A study of teen smoking is planned. Researchers are interested in collecting data which allow them to draw conclusions about the likelihood, frequency, and longevity of teen smoking. The questions asked include: "What is your gender?" "What is your age?" "Do you smoke (yes or no)?" "How many cigarettes per day do you smoke?" "For how long have you smoked (in years)?" What is the measurement scale for each variable?
Answer: Gender: nominal; Age: ratio; Smoking: nominal; Number of cigarettes per day: ratio; Time of smoking: ratio
Q3) Structured data tends to include numbers, dates, and groups of words and numbers called strings.
A)True
B)False
Answer: True
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Page 3
Chapter 2: Tabular and Graphical Methods
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Sample Questions
Q1) A scatterplot depicts a positive ________ relationship, if as x increases, y tends to increase at an increasing rate.
Answer: curvilinear
Q2) A histogram is a series of rectangles where the width and height of each rectangle represent the frequency (or relative frequency) and the width of the respective class.
A)True
B)False
Answer: False
Q3) A ________ ________ is a table that shows the number of data observations that fall into specific interval.
Answer: frequency distribution
Q4) A stem-and-leaf diagram most resembles a(n) ________.
Answer: histogram
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Page 4
Chapter 3: Numerical Descriptive Measures
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Sample Questions
Q1) Geometric mean is greater than the arithmetic mean.
A)True
B)False
Answer: False
Q2) The Sharpe ratio measures the extra reward per unit of risk.
A)True
B)False
Answer: True
Q3) What does the covariance measure?
A) The direction of a linear relationship between two variables.
B) The direction of a curvilinear relationship between two variables.
C) The direction of a linear relationship between two or more variables.
D) The direction of a curvilinear relationship between two or more variables.
Answer: A
Q4) What is the relationship between the variance and the standard deviation?
A) The standard deviation is the absolute value of the variance.
B) The variance is the absolute value of the standard deviation.
C) The variance is the positive square root of the standard deviation.
D) The standard deviation is the positive square root of the variance.
Answer: D
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Chapter 4: Introduction to Probability
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Sample Questions
Q1) Based on his batting average, a baseball player has a 32.7% chance of hitting the ball on his next at bat. Find the odds against this player getting a hit.
Q2) The union of events A and B, denoted by A B, ________. A) contains all outcomes that are in A or B B) contains all outcomes of an experiment C) contains no outcomes that are in A and B D) consists only of outcomes that are in A and B
Q3) An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market in 2016.
With 0.32 probability, foreclosures will increase in Las Vegas.
With 0.46 probability, foreclosures will increase in Las Vegas or the Inland Empire.
With 0.27 probability, foreclosures will increase in Las Vegas and the Inland Empire. What is the probability that foreclosures will increase in the Inland Empire?
Q4) A(n) ________ probability is calculated as the relative frequency with which an event occurs.
Q5) Probabilities can be expressed as fractions, percentages, and ________.
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What is the probability that exactly four residents were unemployed?
A) 0.0013
B) 0.0091
C) 0.0459
D) 0.1468
Q2) A bank manager estimates that an average of two customers enters the tellers' queue every five minutes. Assume that the number of customers that enters the tellers' queue is Poisson distributed. What is the probability that fewer than two customers enter the queue in a randomly selected five-minute period?
A) 0.1353
B) 0.2707
C) 0.4060
D) 0.6767
Q3) A continuous random variable X assumes an (infinitely) uncountable number of distinct values.
A)True
B)False
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) After a heavy snow, the city of Boston spends millions of dollars plowing the streets. Suppose the amount of time the city must spend before the streets are clear follows a log-normal distribution. Further suppose that the average amount of time is 12 hours and the standard deviation is 5 hours. What percentage of the time does it take more than 10 hours for the streets to be cleared?
Q2) The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than five hours to construct a soapbox derby car.
A) 0
B) 0.0228
C) 0.4772
D) 0.9772
Q3) The z table provides ________ probabilities for positive and negative values of z.
Q4) The average wait time at a McDonald's drive-through window is about three minutes ("The Doctor Will See You Eventually," The Wall Street Journal, October 18, 2010). Suppose the wait time is exponentially distributed. What is the probability that a randomly selected customer will have to wait no more than five minutes?
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.
A)True
B)False
Q2) The ________ variation in the production process is caused by specific events or factors that can usually be identified and eliminated.
Q3) A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is ________.
A) 0.3415
B) 0.4082
C) 0.6591
D) 1
Q4) If the expected value of a sample mean equals the population mean, the sample mean is biased.
A)True
B)False
Q5) Stratified random sampling is preferred when the objective is to ________.
Q6) Cluster sampling is preferred when the objective is to ________.
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Chapter 8: Interval Estimation
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Sample Questions
Q1) The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.
A)True
B)False
Q2) A sample of holiday shoppers is taken randomly from a local mall to determine the average daily spending on gifts. From a preselected sample, the standard deviation was determined to be $26. You would like to construct a 95% confidence interval for the mean daily spending on all holiday spending.
A) Find the appropriate sample size necessary to achieve a margin of error of $5. B) Find the appropriate sample size necessary to achieve a margin of error of $8.
Q3) Newscasters wish to predict the outcome of the next presidential election with 95% confidence and a margin of error equal to 0.08. Find the appropriate sample size to accomplish this goal.
Q4) The t distribution table lists t<sub>df</sub> values for selected lower-tail probabilities and degrees of freedom df.
A)True
B)False
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Chapter 9: Hypothesis Testing
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Sample Questions
Q1) A hairdresser believes that she is more profitable on Tuesdays, her lucky day of the week. She knows that, on average, she has a daily revenue of $250. She randomly samples the revenue from eight Tuesdays and finds she takes in $260, $245, $270, $260, $295, $235, $270, and $265. Assume that daily revenue is normally distributed.
A) Specify the population parameter to be tested.
B) Specify the null and alternative hypotheses to test the hairdresser's claim.
C) Calculate the sample mean revenue and the sample standard deviation.
D) Compute the value of the appropriate test statistic.
E) At the 10% significance level, calculate the p-value.
F) At the 10% significance level, is the hairdresser's claim supported by the data?
Q2) A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.
A)True
B)False
Q3) We define the allowed probability of making a Type I error as , and we refer to 100 % as the ________.
Q4) A(n) ________ error is committed when we reject the null hypothesis when the null hypothesis is true.
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Chapter 10: Statistical Inference Concerning Two Populations
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Sample Questions
Q1) Weather forecasters would like to report on temperatures in Washington, DC. In particular, they would like to compare the temperatures in December to temperatures in January to help potential tourists understand whether there is a difference. The average December temperature in a random sample of 16 days is 35 and the average January temperature in a random sample of 20 days is 33. The standard deviations based on historic information are 4 for December and 5 for January.
A) Construct a 90% confidence interval for the difference between the population mean temperatures in December and January.
B) Can we conclude with 90% confidence that the mean temperatures in December and January are different?
Q2) For a hypothesis test about the difference of two proportions, the standard error can be improved on when the hypothesized difference does not equal zero.
A)True
B)False
Q3) To use R for solving hypothesis tests for the difference between two means, use the function ________.
Q4) A common case of dependent sampling is usually referred to as ________ sampling.
Page 12
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Chapter 11: Statistical Inference Concerning Variance
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Sample Questions
Q1) Find the value x for which
A) P(F<sub>(6.4)</sub> x) = 0.01.
B) P(F<sub>(6.4)</sub> < x) = 0.01.
C) P(F<sub>(7.9)</sub> x) = 0.10.
D) P(F<sub>(6.4)</sub> < x) = 0.10.
Q2) Which of the following is a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population?
A) [8.308, 86.207]
B) [7.476, 77.512]
C) [8.617, 78.125]
D) [7.755, 70.313]
Q3) How does the width of the interval respond to the changes in the confidence level?
A) The width of the interval decreases with an increase in the confidence level.
B) The width of the interval increases with an increase in the confidence level.
C) The width of the interval is halved with the increase in the confidence level.
D) The width of the interval is doubled with the decrease in the confidence level.
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Chapter 12: Chi-Square Tests
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Sample Questions
Q1) MARS claims that Skittles candies should be comprised of 30% purple, 10% orange, and 20% should be red, yellow, and green. Business students count a large bag of Skittles and find 265 red, 279 purple, 303 yellow, 271 green, and 212 orange candies.
A) Set up the competing hypotheses to test if at least one proportion is different than the value claimed by MARS.
B) Calculate the value of the test statistic and determine the degrees of freedom.
C) Compute the p-value. Does the evidence suggest that at least one proportion is different from the claimed value at the 5% significance level?
Q2) For the chi-square test of a contingency table, the expected cell frequencies are found as ________.
A) the row total multiplied by the column total divided by the sample size
B) the observed cell frequency
C) (r 1)(c 1)
D) rc
Q3) The chi-square goodness-of-fit test is a right-tailed test.
A)True
B)False
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Chapter 13: Analysis of Variance
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Sample Questions
Q1) For a two-way ANOVA with no interaction, which of the following is the correct formula for the error sum of squares SSE?
A) SSE = SST - (SSA + SSB + SSAB)
B) SSE = SST - (SSA - SSB)
C) SSE = SST + SSA + SSB
D) SSE = SST - (SSA + SSB)
Q2) When using Fisher's Least Significant Difference (LSD) where each interval has an error of , the probability of committing a Type I error for at least one of the individual confidence intervals increases as the number of pairwise comparisons increases.
A)True
B)False
Q3) One-way ANOVA assumes the population standard deviations are unknown and assumed unequal.
A)True
B)False
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Chapter 14: Regression Analysis
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Sample Questions
Q1) A multiple regression model with two explanatory variables is estimated using 20 observations resulting in SSE = 550 and SST = 1000. Which of the following is the correct value of R<sup>2</sup>?
A) 0.10
B) 0.45
C) 0.55
D) 0.90
Q2) The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as s<sub>x </sub>= 35.77, s<sub>y </sub>= 13.34, s<sub>xy </sub>= 447.68. Which of the following is the value of the sample correlation coefficient?
A) 0.88
B) 0.94
C) 0.78
D) 0.78
Q3) If the ________ is substantially greater than zero and the number of explanatory variables is large compared with sample size, then the adjusted R<sup>2</sup> will differ substantially from R<sup>2</sup>.
Q4) We use ________ to derive the coefficient of determination.
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Chapter 15: Inference With Regression Models
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Sample Questions
Q1) The term BLUE stands for Best Linear Unbiased Estimator.
A)True
B)False
Q2) For a given confidence level, the prediction interval is always wider than the confidence interval because ________.
A) the confidence interval is for a particular value of y rather than for the expected value E(y)
B) the prediction interval is for a particular value of y rather than for the expected value E(y)
C) the confidence interval is for a particular value of x rather than for the expected value E(x)
D) the prediction interval is for a particular value of x rather than for the expected value E(x)
Q3) Conditional on x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>k</sub>, the error term is ________ distributed.
Q4) The ________ model is a complete model that imposes no restrictions on the coefficients.
Q5) It is common to refer to the interval estimate for an individual value of y as the ________ interval.
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Chapter 16: Regression Models for Nonlinear Relationships
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Sample Questions
Q1) A model with one explanatory variable that has been log transformed is called a(n)
A) log-log model
B) logarithmic model
C) exponential model
D) linear model
Q2) For the exponential model ln(y) = <sub>0</sub> + <sub>1</sub>x + , if x increases by one unit, then E(y) changes by approximately
A) <sub>1</sub> × 100%
B) <sub>1 </sub>× 100 units
C) <sub>1</sub>%
D) <sub>1 </sub>units
Q3) The quadratic regression model allows for one change in ________.
Q4) The fit of the models y = <sub>0</sub> + <sub>1</sub>x + and y = <sub>0</sub> + <sub>1</sub>ln(x) + can be compared using the coefficient of determination R<sup>2</sup>.
A)True
B)False
Q5) The log-log regression model is ________ in the variables.
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Chapter 17: Regression Models With Dummy Variables
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Q1) Using a ________ we can determine if a particular dummy variable is statistically significant.
Q2) For the model y = <sub>0 </sub>+ <sub>1</sub>x + <sub>2</sub>d + <sub>3</sub>xd+ , in which d is a dummy variable, we cannot perform the F test for the joint significance of the dummy variable d and the interaction variable xd.
A)True
B)False
Q3) For the model y = <sub>0 </sub>+ <sub>1</sub>x + <sub>2</sub>d + <sub>3</sub>xd + , the dummy variable d causes only a shift in intercept.
A)True
B)False
Q4) Gender is an example of ________ variable.
Q5) Regression models that use a binary variable as the response variable are called binary choice models.
A)True
B)False
Q6) The logit model cannot be estimated with standard ________ least squares procedures.
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) A time series is ________.
A) any set of data recorded at the same point in time
B) a set of sequential observations of a variable over time
C) a set of randomly measured data points of multiple variables at the same point in time
D) any set of data collected without regard to differences in time
Q2) When the model y<sub>t</sub> = T<sub>t</sub> × S<sub>t</sub> × I<sub>t</sub> is assumed, to identify the ________, we have to find the seasonally adjusted series.
A) random component
B) seasonality
C) residuals
D) trend
Q3) Which of the following is an example of a time series?
A) The number of daily visitors to the Niagara Falls during the month of April.
B) The recorded exam scores of students in a class.
C) The sales prices of single family homes sold last month in Florida.
D) The current average prices of regular gasoline in different states of the U.S.
Q4) The seasonal component typically represents repetitions over a ________ period.
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Chapter 19: Returns, Index Numbers, and Inflation
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Q1) Rates of return expressed in nominal terms do not represent a true picture because they are not adjusted for inflation.
A)True
B)False
Q2) Timothy Keating invested $120 in buying a share of company X in June last year. Although the company had announced that it will not pay any dividend, the price of this share has increased over the last few months and is expected to go up to $140 by June this year. If the expected annual inflation rate in June this year is 5%, calculate Timothy's real rate of return from this investment if he sells the share at $140.
A) 11.11%
B) 14.29%
C) 22.22%
D) 10%
Q3) If the average price for gasoline in 2001 and 2006 was $1.46 per gallon and $2.59, respectively, the simple price index for 2006 is ________%.
Q4) The ________ equation is a theoretical relationship between nominal returns, real returns, and the expected inflation rate.
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Chapter 20: Nonparametric Tests
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Q1) The Wilcoxon rank-sum test is used as a nonparametric counterpart to the matched-pairs t test.
A)True
B)False
Q2) SHY (NYSEARCA: SHY) is a 1 3-year Treasury bond fund that is considered to be a market-neutral position. Using the S&P 500 as a benchmark and five years of monthly log-return data, the rank correlation coefficient of SHY with the S&P 500 is found to be r<sub>s</sub> = -0.284. The p-value for the test is ________.
A) less than 0.01
B) between 0.01 and 0.05
C) between 0.05 and 0.10
D) greater than 0.10
Q3) Parametric tests are distribution-free tests.
A)True
B)False
Q4) For the Spearman rank correlation test we can use the normal distribution approximation to implement a z test only if n is greater or equal to ________.
Q5) The Kruskal-Wallis test is always a ________-tailed test.
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