Statistics for Business Decision Making Exam
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Course Introduction
Statistics for Business Decision Making explores the fundamental concepts and methods of statistics as they apply to business scenarios. The course covers data collection, organization, and analysis, emphasizing descriptive statistics, probability distributions, hypothesis testing, and regression analysis. Students learn to interpret statistical findings and apply them to real-world business decisions, such as market analysis, quality management, and operations. Through practical examples and case studies, the course equips students with the skills necessary to make informed, data-driven 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) A major portion of ________ is concerned with the problem of estimating population parameters or testing hypothesis about such parameters.
A) descriptive statistics
B) population statistics
C) inferential statistics
D) business statistics
Answer: C
Q2) A respondent of a survey is asked whether the Philadelphia Flyers' performance in the last game was excellent, good, fair, or poor. The person indicates that the performance was "good." This is an example of
A) nominal data
B) ordinal data
C) interval data
D) ratio data
Answer: B
Q3) Time series data contain values of a characteristic of a subject over time.
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) Which of the following is not a graphical technique to display quantitative data?
A) Stem-and-leaf
B) histogram
C) scatterplot
D) bar chart
Answer: D
Q2) A scatterplot depicts a positive ________ relationship, if as x increases, y tends to increase at an increasing rate.
Answer: curvilinear
Q3) For quantitative data, a cumulative relative frequency distribution records the proportion (fraction) of values that fall below the upper limit of each class.
A)True
B)False
Answer: True
Q4) A stem-and-leaf diagram most resembles a(n) ________.
Answer: histogram
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Chapter 3: Numerical Descriptive Measures
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Sample Questions
Q1) Approximately 60% of the observations in a data set fall below the 60th percentile.
A)True
B)False
Answer: True
Q2) The geometric mean is a multiplicative average of a data set used to measure values over a period of time.
A)True
B)False
Answer: True
Q3) Geometric mean is greater than the arithmetic mean.
A)True
B)False
Answer: False
Q4) The z-score has no units even though the original values will normally be expressed in units such as dollars, years, pounds, or calories.
A)True
B)False
Answer: True
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Page 5
Chapter 4: Introduction to Probability
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Sample Questions
Q1) Exams are approaching and Helen is allocating time to studying for exams. She thinks that with the appropriate amount of studying, she has a 70% chance of getting an A in Spanish, and a 20% chance of getting a B in Marketing. Assuming she has no obstacles limiting her available time to allocate to each subject, what is the probability that Helen gets an A in Spanish or a B in Marketing?
Q2) Two events A and B can be both mutually exclusive and independent at the same time.
A)True
B)False
Q3) The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?
A) 0.25
B) 0.33
C) 0.50
D) 0.75
Q4) The union of two events A and B, denoted by A B, does not have outcomes from both A and B.
A)True
B)False
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) Sam is a trucker and believes that for every 60 miles he drives on the freeway in Indiana, there is an average of two state troopers checking his speed with a radar gun.
A) What is the probability that at least one trooper is checking his speed on a randomly selected 60-mile stretch?
B) What is the probability that exactly three troopers are checking his speed on a randomly selected 60-mile stretch?
C) Sam drives 240 miles a day. What is the average number of state troopers who check his speed on a given day?
D) Sam drives 240 miles a day. What is the probability that exactly five troopers check Sam's speed on a randomly selected day?
Q2) Studies have shown that bats can consume an average of 10 mosquitoes per minute. What is the probability that a bat consumes four mosquitoes in a 30-second interval?
A) 0.1404
B) 0.1755
C) 0.3159
D) 0.0189
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) Scores on a business statistics final exam are normally distributed with a mean of 74 and standard deviation of 8. z value for the exam score of 84 equals ________.
Q2) The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?
A) 1.96
B) 1.96
C) 45,100
D) 54,900
Q3) The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata.com). In 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year?
Q4) For < 1, the lognormal distribution somewhat resembles the ________ distribution.
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Page 8
Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) In a small town, there are 3,000 registered voters. An editor of a local newspaper would like to predict the outcome of the next election; in particular, he is interested in the likelihood that Eli Brady will be elected. The editor believes that Eli, a local hero, will garner 54% of the vote. A poll of 500 registered voters is taken.
Assuming that the editor's belief is true, calculate:
A) The expected value and the standard deviation (standard error) of the sample proportion.
B) The probability that the sample proportion score is more than 0.58.
Q2) A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?
A) 1.85
B) 3.41
C) 4
D) 16
Q3) A point estimator refers to an estimator that provides a single value.
A)True
B)False
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9
Chapter 8: Interval Estimation
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Sample Questions
Q1) For a given confidence level 100(1 - )% and population standard deviation , the width of the confidence interval for the population mean is wider, the smaller the sample size n.
A)True
B)False
Q2) For a given confidence level 100(1 - )% and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation .
A)True
B)False
Q3) A confidence interval is generally associated with a(n) ________.
Q4) A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been ________.
A) wider; bigger
B) wider; smaller
C) narrower; bigger
D) narrower; smaller
Q5) The confidence coefficient is equal to ________.
Page 10
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Chapter 9: Hypothesis Testing
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Sample Questions
Q1) It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician's claim.
A) H<sub>0</sub>: p = 0.50 and H<sub>A</sub>: p 0.50
B) H<sub>0</sub>: p 0.50 and H<sub>A</sub>: p > 0.50
C) H<sub>0</sub>: p 0.50 and H<sub>A</sub>: p > 0.50
D) H<sub>0</sub>: p 0.50 and H<sub>A</sub>: p < 0.50
Q2) A doctor thinks he has found a miraculous cure for rheumatoid arthritis. He thinks it will cure more than 50% of all cases within a year of first taking the drug. To test his drug, he runs a clinical trial on 400 patients with rheumatoid arthritis. He finds that 208 of the patients are symptom free within a year.
A) Specify the null and alternative hypotheses to determine whether the proportion of patients that are cured by the drug exceeds 50%.
B) Calculate the value of the test statistic, and find the p-value at a 5% significance level.
C) At the 5% significance level, can you conclude that the percentage of patients who are cured by the drug exceeds 50%?
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Chapter 10: Statistical Inference Concerning Two Populations
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Sample Questions
Q1) A veterinarian wants to know if pit bulls or golden retrievers have a higher incidence of tooth decay at the age of three. The veterinarian surveys 120 three-year-old pit bulls and finds 30 of them have tooth decay. The veterinarian then surveys 160 three-year-old golden retrievers and finds 32 of them have tooth decay. Number the population of pit bulls and golden retrievers by 1 and 2, respectively. At the 10% significance level, can the veterinarian conclude the proportion of pit bulls that have tooth decay is different than the proportion of golden retrievers that have tooth decay?
A) No, because the confidence interval contains zero.
B) Yes, because the confidence interval contains zero.
C) No, because the confidence interval does not contain zero.
D) Yes, because the confidence interval does not contain zero.
Q2) A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?
A) A hypothesis test for p<sub>1</sub> - p<sub>2</sub>.
B) A hypothesis test for <sub>1</sub> - <sub>2</sub>.
C) A matched-pairs hypothesis test for <sub>D</sub>.
D) We are unable to conduct a hypothesis test because the samples would not be independent.
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Chapter 11: Statistical Inference Concerning Variance
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Sample Questions
Q1) Use the R function ________ to obtain a p-value for a test about the ratio of two population variances.
Q2) The following data, drawn from a normal population, are the waiting times (in minutes) of 12 randomly selected customers at a travel desk.
A) Calculate the point estimates of the population variance and the population standard deviation.
B) Compute a 90% confidence intervals for the population variance and the population standard deviation.
Q3) Statistical inference for <sup>2</sup> is based on the F distribution.
A)True
B)False
Q4) Use the F table to approximate these probabilities.
A) P(F<sub>(8,12)</sub> 2.85)
B) P(F<sub>(8,12)</sub> < 0.4)
C) P(F<sub>(5,5)</sub> 7.15)
D) P(F<sub>(5,5)</sub> < 0.09)
Q5) We can use Excel's function ________ that returns the right-tailed probability of the chi-square distribution.
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Chapter 12: Chi-Square Tests
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Sample Questions
Q1) For a chi-square test of a contingency table, each expected frequency must be at least 3.
A)True
B)False
Q2) The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.
A)True
B)False
Q3) The chi-square goodness-of-fit test is a right-tailed test.
A)True
B)False
Q4) For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.
A)True
B)False
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Page 14
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 degrees of freedom when computing MSE?
A) n<sub>T</sub> - c - r + 1
B) n<sub>T</sub> - 1
C) (c - 1)(r - 1)
D) cr(w - 1)
Q2) When using Fisher's LSD method with a given significance level for each interval, the probability of committing a Type I error for at least one comparison increases as the number of ________.
A) pairwise comparisons decreases
B) pairwise comparisons increases
C) sample size increases
D) treatments decreases
Q3) One-way ANOVA is used to determine if differences exist between the means of three or more populations under dependent sampling.
A)True
B)False
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Chapter 14: Regression Analysis
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Sample Questions
Q1) The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of 0.60.
A)True
B)False
Q2) The capital asset pricing model is given by R - R<sub>f</sub> = + (R<sub>M</sub>R<sub>f</sub>) + , where R<sub>M </sub>= expected return on the market, R<sub>f </sub>= risk-free market return, and R = expected return on a stock or portfolio of interest. The explanatory variable in this model is ________.
A) R
B) R - R<sub>f</sub> <sub> <sub
C)</sub><sub> R</sub><sub>M</sub> <sub>
D)</sub><sub> R</sub><sub>M</sub> - R<sub>f</sub>
Q3) Consider the following simple linear regression model: y = <sub>0</sub> + <sub>1</sub>+ . The response variable is ________.
A) y
B) x C)
D) <sub>0</sub>
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Page 16
Chapter 15: Inference With Regression Models
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Sample Questions
Q1) ________ plots can be used to detect common violations, and they can be used to detect outliers.
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) In regression, the predicted values concerning y are subject to ________.
A) kurtosis
B) skewness
C) mean deviation
D) sampling variation
Q4) 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) What R function is used to fit a quadratic regression model?
A) lm
B) predict
C) summary
D) cor
Q2) The log-log and the ________ models can have similar shapes.
Q3) A model in which the response variable has been log transformed is called a(n)
A) log-log model
B) logarithmic model
C) exponential model
D) linear model
Q4) Which of the following regression models is a first-order polynomial?
A) y = <sub>0</sub> +
B) y = <sub>0</sub> + <sub>1</sub>x +
C) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup>+
D) y = <sub>0</sub> + <sub>1</sub>x + <sub>2</sub>x<sup>2</sup> + <sub>3</sub>x<sup>3</sup> +
Q5) When not all variables are transformed with logarithms, the models are called ________ models.
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Chapter 17: Regression Models With Dummy Variables
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Sample Questions
Q1) Consider the regression model y = <sub>0 </sub>+ <sub>1</sub>x + <sub>2</sub>d + <sub>3</sub>xd + . If the dummy variable d changes from 0 to 1, the estimated changes in the intercept and the slope are b<sub>0 </sub>+ b<sub>2</sub> and b<sub>2</sub>, respectively.
A)True
B)False
Q2) Using a ________ we can determine if a particular dummy variable is statistically significant.
Q3) For the linear probability model y = <sub>0</sub> + <sub>1</sub>x + , the predicted value of y is always constrained to be ________.
A) between 0 and 1.
B) positive.
C) negative.
D) between minus infinity to infinity.
Q4) 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
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) The seasonal component typically represents repetitions over a ________ period.
Q2) The exponential trend model is attractive when the increase in the series gets larger over time.
A)True
B)False
Q3) The exponential smoothing method weighs all available observations in a time series equally.
A)True
B)False
Q4) Which of the following factors refers to quantitative forecasting methods?
A) Judgment of the forecaster.
B) A formal model for analyzing historical data.
C) Prior experience of the forecaster.
D) Expertise of the forecaster.
Q5) The regression y<sub>t</sub> = <sub>0</sub> + <sub>1</sub>y<sub>t</sub><sub>-1</sub> + <sub>t </sub>is referred to as a(n) ________ model of order one.
Q6) When comparing polynomial trend models, we use adjusted R<sup>2</sup>, which imposes a penalty for ________.
Q7) The mean of the absolute residuals defines the ________.
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Chapter 19: Returns, Index Numbers, and Inflation
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Sample Questions
Q1) Almas Mohammed paid $50 for a stock of Jones Inc. and expects to earn an annual dividend of $5. If the price of the stock increases to $55 in a year's time, compute the real rates of return from this investment if:
A) the expected inflation rate a year from now is 1.25%.
B) the expected inflation rate a year from now is 3%.
Q2) Sales revenue of firm X was $10 million in 2007. In 2010, the same firm reported higher sales revenue of $15 million. The producer price indices for 2007 and 2010 were 130 and 135.
A) Compute the nominal increase in sales revenue between 2007 and 2010.
B) Compute the real increase in sales revenue between 2007 and 2010.
Q3) If the nominal rate of return is positive, then the real rate of return must also be positive.
A)True
B)False
Q4) The weighted aggregate price index assigns a lower weight to the items that are sold in higher quantities.
A)True
B)False
Q5) The ________ rate is the percentage rate of change of a price index over time.
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Chapter 20: Nonparametric Tests
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Sample Questions
Q1) The null hypothesis of the Wald-Wolfowitz runs test is the elements do not occur randomly.
A)True
B)False
Q2) Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return low-risk return, the value of the test statistic is T = T<sup>+</sup> = 185.
Given the sample size, the sampling distribution of T can be approximated by the normal distribution as the sample size is greater than 10; T can be assumed to follow the normal distribution with mean and standard deviation ________, respectively.
A) 126.5 and 30.80
B) 30.80 and 126.5
C) 125.5 and 948.75
D) 30.80 and 984.75
Q3) If we have a matched-pairs sample of ordinal data, we can use the sign test to determine whether there are significant differences between the ________.
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