Statistical Methods in Business
Exam Materials
Course Introduction
This course provides an in-depth exploration of fundamental and advanced statistical techniques used in business decision-making. Students will learn how to collect, analyze, interpret, and present business data employing methods such as descriptive statistics, probability distributions, hypothesis testing, regression analysis, and forecasting. Emphasis is placed on applying statistical tools to real-world business scenarios, enabling students to make data-driven decisions in areas such as marketing, finance, and operations. The course integrates the use of statistical software to reinforce concepts and develop practical analytical skills relevant to contemporary business environments.
Recommended Textbook
Introduction to Business Statistics 7th Edition by Ronald M. Weiers
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Chapter 1: A Preview of Business Statistics
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Sample Questions
Q1) A survey that asks the respondent to indicate the number of cats in the household is an example of which type of variable?
A) discrete qualitative
B) continuous qualitative
C) discrete quantitative
D) continuous quantitative
Answer: C
Q2) Which of the following sample statistics is a measure of spread (dispersion)?
A) Sample mean
B) Sample standard deviation
C) Sample median
D) Sample proportion
E) Sample mode
Answer: B
Q3) Unlike many other pursuits,improper actions in business statistics can sometimes work in your favor.
A)True
B)False
Answer: True
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Chapter 2: Visual Description of Data
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Sample Questions
Q1) The width (class interval)of a frequency distribution class is the difference between the smallest and largest values in a data set.
A)True
B)False
Answer: False
Q2) A grocery store's monthly sales (in thousands of dollars)for the last year was as follows:
\[\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline \begin{array} { l }
\text { Munt } \\ \mathrm { h }
\end{array} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline \text { Sale5 } & 7 & 74 & 83 & 87 & 85 & 93 & 100 & 105 & 103 & 89 & 78 & 94 \\ \hline
\end{array}\] Construct a line graph for these data.
Answer: 11ea83ae_4657_0e65_908c_9daf104a87be_TB6252_00_TB6252_00
Q3) The ____________________ is also known as the contingency table.
Answer: cross-tabulation
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Chapter 3: Statistical Description of Data
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Sample Questions
Q1) If the coefficient of correlation r is negative,the dependent variable y and the independent variable x are said to be ____________________ related.
Answer: inversely
Q2) Measures of central tendency and dispersion determined from frequency distributions are only approximations of the actual values.
A)True
B)False
Answer: True
Q3) Consider the following sample data: 4,14,6,9,21,3,7,and 10.
What is the mode?
Answer: There is no modal value.
Q4) A sample of 13 measurements has a mean of 28 and a standard deviation of 3.50.Suppose that the sample is enlarged to 15 measurements,by including two additional measurements having common value of 28 each.
A)Find the mean of the sample of 15 measurements.
B)Find the standard deviation of the sample of 15 measurements.
Answer: 28; 3.24
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Chapter 4: Data Collection and Sampling Methods
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Sample Questions
Q1) Factor analysis is a set of techniques for studying interrelationships among variables.This is done by reducing a very large set of variables to a smaller set of new variables (factors)that are more basic in meaning but contain most of the information in the original set.
A)True
B)False
Q2) In experiments,the purpose is to identify ____________________ and ____________________ relationships between variables.
Q3) To overcome one of the shortcomings of telephone surveys due to unlisted telephone numbers:
A) survey takers purchase mail lists of unlisted telephone number subscribers.
B) survey takers employ random digit dialing facilities.
C) survey takers contact telephone companies for a list of unlisted telephone numbers.
D) survey takers purchase lists of unlisted telephone numbers from magazine subscribers.
E) survey takers go door to door and identify the unlisted telephone subscribers.
Q4) What is data warehouse?
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Chapter 5: Probability: Review of Basic Concepts
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Sample Questions
Q1) Determine the probability of event A.
Q2) Machines
Machine A produces 3% defectives,machine B produces 5% defectives,and machine C produces 10% defectives.Of the total output from these machines,60% of the items are from machine A,30% from B,and 10% from C.One item is selected at random from a day's production.
What is the prior probability that the item came from machine A?
Machine B?
Machine C?
Q3) If the odds in favor of an event happening are A:B,what is the probability being expressed?
Q4) The ____________________ of events describes the case where two or more events occur at the same time.
Q5) For a randomly selected consumer,find the following probability: P(A or D).
Q6) Determine the probability that a randomly selected bond will have a rate of interest of ten percent up to but not including 14 percent.
Q7) Compute P(S).
Q8) Compute P(A<sub>2</sub> and B).
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Q9) Apply Bayes' theorem to compute the posterior probability P(A<sub>3</sub> / B).
Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) Assume that you used Minitab statistical package to generate the individual binomial probabilities when n = 100 and \(\pi\) = .042,and then generate the individual Poisson probabilities for \(\lambda\) = 4.2.Do you expect the probabilities obtained in both cases to be similar or different? Explain.
Q2) What are the parameters of a random variable described by the binomial distribution?
Q3) What is the probability that a randomly selected Egyptian household will have between 2 and 4 children?
Q4) In an intermediate level economics class there are 18 students.Nine of these are economics majors.For class discussion purposes three students are randomly selected.What is the probability that at least one is an economics major?
Q5) The number of life insurance policy holders is an example of a discrete random variable.
A)True
B)False
Q6) What is the probability that none of the sheets sold are sub-standard?
Q7) What is the probability that at least one T.V.home in the sample is served by cable?
Page 8
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) The average waiting time at the checkout counter for a large grocery chain is 2.45 minutes with a standard deviation of 24 seconds (0.40 minutes).Assume that the distribution of waiting time is normal.What is the probability that a customer must wait more than 3 minutes for check out?
Q2) A statistics class is composed of 60 percent females.If 15 students are selected randomly,what is the probability that this group will include either 8,9,10,or 11 females? Use the normal distribution.
Q3) Let x be a binomial random variable.Find P(x 40)if n = 100 and \(\pi\) = 0.32.
Q4) The mean of the exponential distribution is the inverse of that of the normal distribution.
A)True
B)False
Q5) There exists a different normal curve for every possible pair of \(\mu\) and \(\text { ?}\) .
A)True
B)False
Q6) Explain why the total area beneath a probability density function is equal to 1.0.
Q7) For the standard normal curve,determine the area to the right of z = 0.34.
Page 9
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Chapter 8: Sampling Distributions
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Sample Questions
Q1) Fifty percent of all college students attend schools within 50 miles of their homes.In a sample of 500 college students,the probability that the sample proportion will be between 0.45 and 0.55 is:
A) 0.4875.
B) 0.9818.
C) 0.4909.
D) 0.9750.
E) 0.5000.
Q2) A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10.The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:
A) 0.0166.
B) 0.0228.
C) 0.3708.
D) 0.0394.
Q3) Using information from a sample to reach conclusions about the population from which it was drawn is referred to as ____________________.
Q4) Calculate the mean of the sample means.
Q5) State the central limit theorem.
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Chapter 9: Estimation From Sample Data
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Sample Questions
Q1) If a sample containing 12 observations is taken from a normally distributed population and a 99% confidence estimate for \(\mu\) is needed,the appropriate t-score is:
A) 2.681.
B) 2.718.
C) 3.169.
D) 3.055.
E) 3.106.
Q2) The appropriate procedure for constructing an interval estimate for the population mean depends largely on whether the population standard deviation \(\text { ? }\) is known.
A)True
B)False
Q3) The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 200 had 40 successes is:
A) 0.2554.
B) 0.1446.
C) 0.2465.
D) 0.1535.
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Chapter 10: Hypothesis Tests Involving a Sample Mean or Proportion
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Sample Questions
Q1) A random sample of 10 observations was drawn from a large population.The data values were: 6,4,4,7,5,5,4,5,6,and 4 Test to determine if we can infer at the 5% significance level that the population mean is less than 6.
Q2) H<sub>0</sub>: \(\mu \leq \mu _ { 0 }\) ,H<sub>1</sub>: \(\mu > \mu _ { 0 }\) ; n > 30 and \(\alpha\) = 0.01
State the appropriate decision rule.
Q3) What is the conclusion?
Q4) State your conclusion.
Q5) For a sample of 36 items from a population for which the standard deviation \(\alpha = 12\) the sample mean is 350.Use the 95% confidence interval to test the hypothesis H<sub>0</sub>: \(\mu\) = 400 versus H<sub>1</sub>: \(\mu \neq\) 400 at the \(\alpha\) = .05 level of significance.
Q6) Calculate the test statistic and write your conclusion.
Appropriate test: ____________________
Test statistic = ____________________
Conclusion: __________________________
Page 12
Q7) It has been claimed that no more than 3% of the units coming off an assembly line are defective.Will this test be a one-tail - left,a one tail - right,or a two-tail? Explain your answer.
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Chapter 11: Hypothesis Tests Involving Two Sample Means
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Sample Questions
Q1) Estimate with 95% confidence the difference in coffee breaks mean time between the two groups.
Q2) What is the conclusion?
Q3) State the decision rule.
Q4) Use a 0.01 significance level to determine if there is sufficient evidence to conclude that a difference in proportions exists.What is the random variable?
Q5) Use \(\alpha\) = 0.05.State the decision rule in terms of the critical value.
Q6) In testing the difference between two population means using two independent samples,the sampling distribution of the sample mean difference \(\overline { \mathrm { x } } _ { 1 } - \overline { \mathrm { x } } _ { 2 }\) is normal if the:
A) sample sizes are both greater than 30.
B) populations are normal.
C) populations are non-normal and the sample sizes are large.
D) population sizes are both greater than 30.
E) all of these are required conditions.
Q7) What is the decision rule?
Q8) What is the conclusion?
Page 13
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Chapter 12: Analysis of Variance Tests
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Sample Questions
Q1) Develop a randomized block design to test for the difference between the average number of customers per day between four different stores using \(\alpha\) = 0.05 and using the days as the blocking variable. Calculate the block sum of squares.
Q2) The one-way ANOVA is also referred to as the one-factor,completely randomized design,since the treatments are randomly assigned to all of the persons or other test units in the experiment.
A)True
B)False
Q3) A randomized block experiment having five treatments and six blocks produced the following values: SSTR = 287, SST = 1,446, SSE = 180. The value of SSB must be: A)30.
B)979.
C)467.
D)20.
E)107.
Q4) How is two-way ANOVA similar to the randomized block design? How does it differ?
Q5) Compute the test statistic.
Test statistic = ____________________ = ____________________
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Chapter 13: Chi-Square Applications
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Sample Questions
Q1) The goodness-of-fit chi-square test is a two-tailed test.
A)True
B)False
Q2) The chi-square distribution is skewed to the left (negatively skewed),but as degrees of freedom increase,it approaches the shape of the binomial distribution.
A)True
B)False
Q3) A test for independence is applied to a contingency table with 4 rows and 5 columns for two nominal variables.Calculate the degrees of freedom for this test.
Q4) Employing a 0.10 significance level,what is the appropriate conclusion based on the calculations from the above data?
Q5) Using \(\alpha\) = 0.05,state the decision rule in terms of the critical value.
Q6) What is the expected frequency of the $50,000 and over and No categories?
Q7) Do the data provide enough evidence to support the professor's claim?
Q8) State the appropriate conclusion at the 0.05 significance level. The proportions of males and females who are offended by the ads are:
Page 15
Q9) What is the calculated value of the test statistic?
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Chapter 14: Nonparametric Methods
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Sample Questions
Q1) A Wilcoxon rank sum test for comparing two independent samples involves two sample sizes: 8 and 6.The alternate hypothesis is m<sub>1</sub> m<sub>2</sub>.Use a 0.10 significance level.What are the appropriate table values?
Separate your answers with commas,for example x,y,z,etc.
Q2) The test question is: Can we conclude at the 5% significance level that there are differences in service quality among the four airlines? Using the appropriate statistical table,what statement can be made about the p-value for the above test?
Q3) The z-test approximation to the Wilcoxon signed rank test is used whenever the number of nonzero differences is at least ____________________.
Q4) What is the rank assigned to the four observations of value 22?
Q5) Which of the following tests would be an example of a nonparametric method?
A) Wilcoxon signed rank test
B) Kruskal-Wallis test
C) Friedman test
D) Wilcoxon rank sum test
E) All of these are nonparametric methods
Q6) What is a nonparametric test?
Q7) The chapter lists four major advantages to nonparametric testing.What are they?
Page 16
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Chapter 15: Simple Linear Regression and Correlation
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Sample Questions
Q1) Correlation analysis requires that the scales of measurement be expressed in either:
A) nominal or ordinal.
B) ordinal or ratio.
C) interval or ratio.
D) nominal or ratio.
E) nominal or interval.
Q2) Construct a 95% confidence interval for the slope of the population regression line.
Q3) Consider the following data values of variables x and y \[\begin{array} { | l | l | l | l | l | l | }
\hline \mathbf { x } & 4 & 2 & 6 & 4 & 3 \\
\hline \mathbf { y } & 5 & 3 & 7 & 6 & 5 \\
\hline
\end{array}\] Use Excel or Minitab to construct a scatter diagram of the data points
Q4) Determine the standard error of estimate.
Q5) Construct a 95% prediction interval for the mean weekly food expense when the number in household equals 3.
Q6) Find the least-squares regression line.
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Chapter 16: Multiple Regression and Correlation
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Sample Questions
Q1) In interpreting the multiple regression equation,it can be a mistake to conclude that one independent variable is more important than another just because its partial regression coefficient happens to be large.
A)True
B)False
Q2) Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final mark?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________
Q3) In a multiple regression analysis involving 40 observations and 4 independent variables,SST = 375 and SSE = 75.The multiple coefficient of determination is:
A) 0.8333.
B) 0.8000.
C) 0.1875. D) 0.9375.
Q4) How much of the variation in thefts is explained by the model?
Q5) In multiple regression,to what does the descriptor "multiple" refer?
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Chapter 17: Model Building
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Sample Questions
Q1) The model \(\hat { Y }\) = b<sub>0</sub> + b<sub>1</sub>x + b<sub>2</sub>x<sup>2</sup> is referred to as a:
A) simple linear regression model.
B) first order model with one predictor variable.
C) second order model with one predictor variable.
D) third order model with one predictor variable.
Q2) The shape of the model described by the equation \(E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }\) could be:
A) parabolic resembling an upright"U".
B) parabolic resembling an upside-down"U".
C) a straight line with an intercept \(\beta _ { 0 }\) and slope \(\beta _ { 2 } / \beta _ { 1 }\) .
D) a straight line with an intercept \(\beta _ { 0 }\) and slope \(\beta _ { 1 } / \beta _ { 2 } .\).
E) Both A and B.
Q3) If the goal for the regression analysis is simply to predict the value of the dependent variable based on a set of predictor variables,we need not worry about ____________________,which means that some of the predictor variables might be highly correlated with each other.
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Chapter 18: Models for Time Series and Forecasting
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Sample Questions
Q1) According to the chapter,regression models based on time series data are especially susceptible to autocorrelation.Why?
Q2) What is an index number?
Q3) A common method of testing for autocollinearity (serial correlation)is a Durbin-Watson test.
A)True
B)False
Q4) By analyzing a time series,we can identify patterns and tendencies that help explain variation in past sales,shipments,rainfall,or any other variable of interest.
A)True
B)False
Q5) Selecting a large the number of periods (N)for a centered moving average A) results in greater dampening. B) is less responsive to directional changes. C) results in a more accurate forecast.
D) both A and B.
E) All of the above.
Q6) What is the linear trend equation?
Q7) Calculate the seasonal indexes based on the regression trend line.
Page 20
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Chapter 19: Decision Theory
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Sample Questions
Q1) How many shirts should be produced using the minimax regret criterion?
Q2) Convert the payoff table to a regret table
Q3) Which of the following would not be considered a state of nature for a business firm?
A) Federal Reserve regulations.
B) Food and Drug Administration regulations.
C) The number of employees to hire.
D) Minimum wage regulations.
E) What other firms charge for price.
Q4) Bayesian decision making takes into account the probabilities for the respective states of nature.
A)True
B)False
Q5) What decision will be made using the minimax regret criterion?
Q6) What is the most the company should be willing to pay for a research study designed to reduce its uncertainty about media and legal developments concerning packaging?
____________________ million
Q7) What decision will be made using the maximin criterion?
Q8) What price should ABC choose using the maximin criterion?
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Chapter 20: Total Quality Management
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Sample Questions
Q1) When a process that is governed by a Six Sigma approach to quality improvement is found to be in statistical control,the expected number of defects per million products or opportunities is
A) 1.2.
B) 1.5.
C) 2.0.
D) 3.4.
E) 6.0.
Q2) Random variation occurs due to identifiable causes that have changed the process.
A)True
B)False
Q3) Identify the circumstances when the \(\bar{x}\) chart and R chart might be useful.
Q4) Assignable variation occurs due to identifiable causes that have changed the process.
A)True B)False
Q5) Construct the p chart and determine if the production process is under control.
Q6) What is competitive benchmarking,and how can it be used?
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