Introduction to Business Statistics
Exam Solutions
Course Introduction
Introduction to Business Statistics offers students a foundational understanding of statistical concepts and tools as applied in business contexts. The course covers topics such as data collection, organization, and interpretation; descriptive statistics; probability distributions; sampling methods; estimation; hypothesis testing; correlation; and regression analysis. Emphasis is placed on practical application, enabling students to analyze business data, interpret results, and make informed decisions based on statistical reasoning. Through real-world examples and hands-on exercises, students develop the analytical skills necessary to support data-driven strategies in various business environments.
Recommended Textbook
Statistics for Business and Economics 11th Edition by
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Page 2
David R. Anderson
Chapter 1: Data and Statistics
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Sample Questions
Q1) Refer to Exhibit 1-3.Gender is an example of ________ data.
A)nominal
B)ordinal
C)interval
D)ratio
Answer: A
Q2) Some hotels ask their guests to rate the hotel's services as excellent,very good,good,and poor.This is an example of the A)ordinal scale
B)ratio scale
C)nominal scale
D)interval scale
Answer: A
Q3) In experimental studies,the variable of interest
A)is not controlled
B)is controlled
C)must be numerical
D)cannot be numerical
Answer: B
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Chapter 2: Descriptive Statistics: Tabular and Graphical
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Sample Questions
Q1) Categorical data can be graphically represented by using a(n)
A)histogram
B)frequency polygon
C)ogive
D)bar chart
Answer: D
Q2) Refer to Exhibit 2-1.The number of students who work 19 hours or less is
A)80
B)100
C)200
D)400
Answer: B
Q3) In constructing a frequency distribution,as the number of classes are decreased,the class width
A)decreases
B)remains unchanged
C)increases
D)can increase or decrease depending on the data values
Answer: C
Page 4
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Chapter 3: Descriptive Statistics: Numerical Measures
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Sample Questions
Q1) Refer to Exhibit 3-3.The coefficient of variation is
A)72.66%
B)81.24%
C)264%
D)330%
Answer: B
Q2) A numerical measure of linear association between two variables is the A)variance
B)covariance
C)standard deviation
D)coefficient of variation
Answer: B
Q3) The most frequently occurring value of a data set is called the A)range
B)mode
C)mean
D)median
Answer: B
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Chapter 4: Introduction to Probability
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Sample Questions
Q1) In a recent survey in a Statistics class,it was determined that only 60% of the students attend class on Fridays.From past data it was noted that 98% of those who went to class on Fridays pass the course,while only 20% of those who did not go to class on Fridays passed the course.
a.What percentage of students is expected to pass the course?
b.Given that a person passes the course,what is the probability that he/she attended classes on Fridays?
Q2) If A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5,then P(A \(\cup\) B)=
A)0.00
B)0.15
C)0.8
D)0.2
Q3) In an experiment,events A and B are mutually exclusive.If P(A)= 0.6,then the probability of B
A)cannot be larger than 0.4
B)can be any value greater than 0.6
C)can be any value between 0 to 1
D)cannot be determined with the information given
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Chapter 5: Discrete Probability Distributions
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Sample Questions
Q1) Compute the hypergeometric probabilities for the following values of n and x.Assume N = 8 and r = 5.
a.n = 5,x = 2
b.n = 6,x = 4
c.n = 3,x = 0
d.n = 3,x = 3
Q2) Refer to Exhibit 5-8.The expected value of the random variable x is A)2
B)5.3
C)10
D)2.30
Q3) Refer to Exhibit 5-6.The variance of the number of cups of coffee is A).96
B).9798
C)1
D)2.4
Q4) A production process produces 2% defective parts.A sample of 5 parts from the production is selected.What is the probability that the sample contains exactly two defective parts? Use the binomial probability function and show your computations to answer this question.
7
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Chapter 6: Continuous Probability Distributions
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Sample Questions
Q1) The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500.
a.The mayor of Daisy City makes $2,250 a month.What percentage of Daisy City's residents has incomes that are more than the mayor's?
b.Individuals with incomes of less than $1,985 per month are exempt from city taxes.What percentage of residents is exempt from city taxes?
c.What are the minimum and the maximum incomes of the middle 95% of the residents?
d.Two hundred residents have incomes of at least $4,440 per month.What is the population of Daisy City?
Q2) The mean of a standard normal probability distribution
A)is always equal to zero
B)can be any value as long as it is positive
C)can be any value
D)is always greater than zero
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Chapter 7: Sampling and Sampling Distributions
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Sample Questions
Q1) There are 500 employees in a firm,45% are female.A sample of 60 employees is selected randomly.
a.Determine the standard error of the proportion.
b.What is the probability that the sample proportion (proportion of females)is between 0.40 and 0.55?
Q2) As a rule of thumb,the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
A)np \(\ge\) 5
B)n(1 - p) \(\ge\) 5 and n \(\ge\) 30
C)n \(\ge\) 30 and (1 - p)= 0.5
D)None of these alternatives is correct.
Q3) How many simple random samples of size 3 can be selected from a population of size 7?
A)7
B)21
C)35 D)343
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Chapter 8: Interval Estimation
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Sample Questions
Q1) In a sample of 400 voters,360 indicated they favor the incumbent governor.The 95% confidence interval of voters not favoring the incumbent is
A)0.871 to 0.929
B)0.120 to 0.280
C)0.765 to 0.835
D)0.071 to 0.129
Q2) The monthly starting salaries of students who receive an MBA degree have a population standard deviation of $110.What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less?
Q3) Refer to Exhibit 8-4.At 95% confidence,the size of the margin of error is
A)1.96
B)50
C)98
D)42
Q4) As the sample size increases,the margin of error
A)increases
B)decreases
C)stays the same
D)increases or decreases depending on the size of the mean
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Chapter 9: Hypothesis Tests
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Sample Questions
Q1) The sum of the values of \(\alpha\) and \(\beta\)
A)always add up to 1.0
B)always add up to 0.5
C)is the probability of Type II error
D)None of these alternatives is correct.
Q2) A soft drink filling machine,when in perfect adjustment,fills the bottles with 12 ounces of soft drink.Any over filling or under filling results in the shutdown and readjustment of the machine.To determine whether or not the machine is properly adjusted,the correct set of hypotheses is
A)H<sub>0</sub>: \(\mu\) < 12 H<sub>a</sub>: \(\mu\) \(\le\)12
B)H<sub>0</sub>: \(\mu\) \(\le\)
12 H<sub>a</sub>: \(\mu\) > 12
C)H<sub>0</sub>: \(\mu\) \(\neq\)12 H<sub>a</sub>: \(\mu\) = 12
D)H<sub>0</sub>: \(\mu\) = 12 H<sub>a</sub>: \(\mu\) \(\neq\) 12
Q3) Two thousand numbers are selected randomly;960 were even numbers.
a.State the hypotheses to determine whether the proportion of odd numbers is significantly different from 50%.
b.Compute the test statistic.
c.At 90% confidence using the p-value approach,test the hypotheses.
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Chapter 10: Statistical Inference About Means and
Proportions With Two Populations
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Sample Questions
Q1) Refer to Exhibit 10-1.The p-value is
A)0.0668
B)0.0334
C)1.336
D)1.96
Q2) Refer to Exhibit 10-2.The null hypothesis to be tested is H<sub>0</sub>: \(\mu\)<sub>d</sub> = 0.The test statistic is
A)-1.96
B)1.96
C)0
D)1.645
Q3) Refer to Exhibit 10-3.The p-value for the difference between the two population means is
A).0013
B).0026
C).4987
D).9987
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Chapter 11: Inferences About Population Variances
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Sample Questions
Q1) The chi-square value for a one-tailed test (lower tail)when the level of significance is 0.1 and the sample size is 15 is
A)21.064
B)23.685
C)7.785
D)6.571
Q2) Refer to Exhibit 11-2.At 95% confidence the null hypothesis
A)should be rejected
B)should not be rejected
C)should be revised
D)None of these alternatives is correct.
Q3) A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces.A 95% confidence interval estimate of the variance for the population is
A)0.2313 to 0.8533
B)0.2224 to 0.7924
C)0.3042 to 0.5843
D)0.0925 to 0.3413
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Chapter 12: Tests of Goodness of Fit and Independence
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Sample Questions
Q1) Refer to Exhibit 12-5.With a .05 level of significance,the critical value for the test is
A)1.645
B)7.815
C)14.067
D)15.507
Q2) The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is
A)n-1
B)K-1
C)number of rows minus 1 times number of columns minus 1
D)a chi-square distribution is not used
Q3) Refer to Exhibit 12-6.At 95% confidence,the conclusion of the test is that the
A)arrival of cars follows a Poisson distribution
B)arrival of cars does not follow a Poisson distribution
C)test is inconclusive
D)None of these alternatives is correct.
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Chapter 13: Analysis of Variance and Experimental Design
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Sample Questions
Q1) A term that means the same as the term "variable" in an ANOVA procedure is
A)factor
B)treatment
C)replication
D)variance within
Q2) Refer to Exhibit 13-7.The mean square between treatments (MSTR)is
A)36
B)16
C)8
D)32
Q3) An experimental design that permits statistical conclusions about two or more factors is a
A)randomized block design
B)factorial design
C)completely randomized design
D)randomized design
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Chapter 14: Simple Linear Regression
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Sample Questions
Q1) Refer to Exhibit 14-9.The least squares estimate of b<sub>1</sub> equals
A)0.923
B)1.991
C)-1.991
D)-0.923
Q2) In regression analysis,the unbiased estimate of the variance is
A)coefficient of correlation
B)coefficient of determination
C)mean square error
D)slope of the regression equation
Q3) Refer to Exhibit 14-2.The point estimate of y when x = 10 is A)-10
B)10
C)-4
D)4
Q4) The standard error is the
A)t-statistic squared
B)square root of SSE
C)square root of SST
D)square root of MSE
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Chapter 15: Multiple Regression
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Sample Questions
Q1) A regression analysis involved 6 independent variables and 27 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have
A)27 degrees of freedom
B)26 degrees of freedom
C)21 degrees of freedom
D)20 degrees of freedom
Q2) In a multiple regression model,the error term \(\varepsilon\) is assumed to
A)have a mean of 1
B)have a variance of zero
C)have a standard deviation of 1
D)be normally distributed
Q3) A regression model in which more than one independent variable is used to predict the dependent variable is called
A)a simple linear regression model
B)a multiple regression model
C)an independent model
D)None of these alternatives is correct.
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Chapter 16: Regression Analysis: Model Building
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Sample Questions
Q1) Refer to Exhibit 16-1.The coefficient of X<sub>3</sub>
A)is significant
B)is not significant
C)can not be tested,because not enough information is provided D)None of these alternatives is correct.
Q2) Refer to Exhibit 16-4.The model
A)is significant
B)is not significant
C)Not enough information is provided to answer this question.
D)None of these alternatives is correct.
Q3) Refer to Exhibit 16-2.The degrees of freedom associated with SST are A)24
B)6 C)19
D)None of these alternatives is correct.
Q4) Refer to Exhibit 16-2.The value of MSE is A)348
B)10.40
C)10.83
D)32.13
Page 18
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Chapter 17: Index Numbers
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Sample Questions
Q1) The reason why weights are used in an aggregate index is to
A)insure that all items have an influence on the index which is relative to their respective importance
B)insure that expensive items are considered more heavily
C)insure that current prices will influence the index more than base prices
D)None of these alternatives is correct.
Q2) Aggregate price indexes reflecting the prices of stocks listed on the New York Stock Exchange are
A)Stock Exchange indexes
B)Indexes of Industrial Production
C)Producer price indexes
D)Dow Jones averages
Q3) Refer to Exhibit 17-2.The price relative for item Y is
A)66.67
B)1.50
C)40.00
D)150.00
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Chapter 18: Forecasting
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Sample Questions
Q1) Refer to Exhibit 18-3.The intercept,b<sub>0</sub>,is
A)-1.5
B)+1.5
C)8.3
D)-8.3
Q2) Refer to Exhibit 18-1.An estimate of the seasonal-irregular component for Quarter 3 of Year 1 is
A).64
B)1.5625
C)5.333
D)30
Q3) Refer to Exhibit 18-2.The forecast for period 10 is
A)10.0
B)25.0
C)30.0
D)22.5
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Chapter 19: Nonparametric Methods
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Sample Questions
Q1) Refer to Exhibit 19-2.The null hypothesis that is being tested is
A)H<sub>0</sub>: \(\mu\) = 5
B)H<sub>0</sub>: \(\mu\) = 0.5
C)H<sub>0</sub>: P = 5
D)H<sub>0</sub>: P = 0.5
Q2) Refer to Exhibit 19-3.To test the null hypothesis,the appropriate probability distribution to use is
A)normal
B)chi-square
C)t distribution
D)binomial
Q3) Refer to Exhibit 19-4.The test statistic equals
A)-0.81 or 0.81
B)-0.89 or 0.89
C)-10 or 10
D)-20 or 20
Q4) In a sample of 300 shoppers,160 indicated they prefer fluoride toothpaste,120 favored nonfluoride,and 20 were indifferent.At a 0.05 level of significance,test for a difference in the preference for the two kinds of toothpaste.
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Chapter 20: Statistical Methods for Quality Control
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Sample Questions
Q1) A production process is considered in control if no more than 4% of the items produced are defective.Samples of size 100 are used for the inspection process.
a.Determine the standard error of the proportion.
b.Determine the upper and the lower control limits for the P chart.
Q2) The upper and lower control limits of the proportions of defectives of a process are 0.33 and 0.27.
a.What has been the proportion of defectives in this process?
b.What has been the sample size?
Q3) A control chart that is used when the output of a production process is measured in terms of the percent defective is
A)a P chart
B)an X bar chart
C)a process chart
D)None of these alternatives is correct.
Q4) A production process is considered in control if no more than to 6% of the items produced are defective.Samples of size 300 are used for the inspection process.
a.Determine the standard error of the proportion.
b.Determine the upper and the lower control limits for the P chart.
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Chapter 21: Decision Analysis
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Sample Questions
Q1) A decision criterion which weights the payoff for each decision by its probability of occurrence is known as the
A)Payoff criterion
B)expected value criterion
C)probability
D)expected value of perfect information
Q2) Refer to Exhibit 21-2.The recommended decision based on the expected value criterion is
A)A
B)B
C)Both alternatives are the same.
D)None of these alternatives is correct.
Q3) An intersection or junction point of a decision tree is called a (n)
A)junction
B)intersection
C)intersection point
D)node
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Chapter 22: Sample Survey
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Sample Questions
Q1) Any method of sampling for which the probability of selecting a sample can not be computed is termed
A)probability sampling
B)nonprobabilistic sampling
C)unknown population sampling
D)None of these alternatives is correct.
Q2) Refer to Exhibit 22-4.The estimate of the standard error of proportion is
A)0.210
B)0.700
C)0.300
D)0.062
Q3) A list of the sampling units for a study is
A)the sampled population
B)called the frame
C)the same as the sample
D)the sample space
Q4) A community has 2,000 registered voters.A pilot study revealed that 70% of the individuals are planning to vote for the incumbent mayor.We are interested in selecting a sample.So that the sampling error will not exceed 4%,what size sample should be taken?
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