Statistics for Management Solved Exam Questions
Course Introduction
Statistics for Management introduces students to the fundamental statistical concepts and techniques relevant to modern business decision-making. The course covers descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and their applications in management. Emphasis is placed on interpreting data, drawing meaningful conclusions, and effectively communicating statistical findings to inform managerial strategies. Students will engage with real-world case studies, utilize statistical software, and develop problem-solving skills essential for analyzing business data and supporting evidence-based management decisions.
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) 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
Q2) A recent Wall Street Journal poll asked a group of American voters to rate economic conditions in the United States.22% of the respondents rated economic conditions as "favorable." Identify the population,sample,sample statistic,and population parameter in this survey.
Population: ________________________________________
Sample: ________________________________________
Sample statistic: ________________________________________
Population parameter: ________________________________________.
Answer: All eligible voters in the U.S.; Voters selected to participate in the survey.; 22%; The percentage of all voters who would rate economic conditions as favorable.
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Chapter 2: Visual Description of Data
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Sample Questions
Q1) The ____________________ is also known as the contingency table. Answer: cross-tabulation
Q2) A histogram describes a frequency distribution by using a series of adjacent rectangles,each of which has a length that is proportional to the frequency of observations within the range of values it represents.
A)True
B)False
Answer: True
Q3) Discuss the guidelines that are recommended for constructing a frequency distribution.
Answer: The guidelines for constructing a frequency distribution are: a.The set of classes must be mutually exclusive,with no overlaps.b.Set of classes must be exhaustive.c.If possible the classes should have equal widths.d.In general,about 5 to 15 classes will be suitable.e.When possible,class widths should be round numbers.f.Avoid using open-end classes.
Q4) The ____________________ is a diagram in which each point represents a pair of known or observed values of two variables.
Answer: scatter diagram
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Chapter 3: Statistical Description of Data
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Sample Questions
Q1) Consider the following sample data: 4,14,6,9,21,3,7,and 10.
Calculate the mean.
Answer: 9.25
Q2) Sample values of 13 monthly sales figures (in thousands of dollars)are: 6,5,6,6,7,8,9,10,10,10,9,9,and 6.
What is the mode?
____________________ thousand
Answer: 6.00
Q3) Compute the third quartile.
Answer: 26.5
Q4) What are the 1st,2nd,and 3rd quartiles?
Q1 = ____________________
Q2 = ____________________
Q3 = ____________________
Answer: 4808.25; 5263.5; 5745.0
Q5) Calculate the average number of calls per day.
Answer: 4.6 calls per day
Q6) What is the quartile deviation?
Answer: (Q<sub>3</sub> - Q<sub>1</sub>)/2 = 468.375
Page 5
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Chapter 4: Data Collection and Sampling Methods
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Sample Questions
Q1) When is a sample a better choice than a census?
A) When the population is changing over time.
B) When taking the U.S.Census of the population.
C) When some sampling error can be tolerated.
D) When time is an important factor.
E) Each of these is a reason for taking a sample rather than a census.
Q2) The convenience sample is an example of probability sampling where every person or element in the population may not have an equal chance for inclusion in the sample.
A)True
B)False
Q3) ____________________ validity asks whether the results of an experiment can be generalized to other people or settings.
Q4) Regarding causal studies,it should be pointed out that statistical techniques alone can prove causality.
A)True
B)False
Q5) A ____________________ is a characteristic of a sample,while a ____________________ is a characteristic of a population.
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Chapter 5: Probability: Review of Basic Concepts
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Sample Questions
Q1) Determine the probability that a randomly selected bond will have a rate of interest of at least 14 percent,but less than 15 percent.
Q2) According to an old song lyric,"love and marriage go together like a horse and carriage." Let love be event A and marriage be event B.Are events A and B mutually exclusive?
Q3) A survey revealed that 21.5% of the households had no checking account,66.9% had regular checking accounts,and 11.6% had NOW accounts.Of those households with no checking account 40% had savings accounts.Of the households with regular checking accounts 71.6% had a savings account.Of the households with NOW accounts 79.3% had savings accounts. The probability that a randomly selected household has a savings account is:
A) 0.609.
B) 1.000.
C) 0.227.
D) 0.657.
E) 0.537.
Q4) Compute P(B and A<sub>3</sub>).
Q5) Probability refers to a number between ____________________ and ____________________ which expresses the ____________________ that an event will occur.
Page 7
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) What is the probability that at least one is a homemaker?
Q2) Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January Kansas will experience exactly 2 tornadoes is:
A) 0.7913.
B) 0.4076.
C) 0.2087.
D) 0.1304. E) 0.2226.
Q3) The ____________________ probability distribution deals with consecutive trials that are statistically independent,each of which has only two possible outcomes,generally referred to as success or failure.
Q4) What is the probability that a randomly selected Egyptian household will have fewer than 4 children?
Q5) Find the following probabilities:
a.P(X > 1)
b.P(X > 2)
c.P(1\(\le\) X \(\le\) 2)
d.P(0 <X < 1)
e.P(1\(\le\) X \(\le\) 3)
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) The binomial distribution is symmetrical whenever the population proportion \(\pi\) is ____________________,and approaches symmetry for values that are close to
Q2) Assume x is normally distributed with mean \(\mu\) = 15 and standard deviation \(\text { }\) = 3.Use the approximate areas beneath the normal curve,as discussed in this section,to find P(12 x 18).
Q3) A dispatcher for an airport shuttle averages sending a van to the airport 2 times every 60 minutes.The distribution is Poisson,and the driver must take a 15-minute lunch break.The probability that he can finish lunch before getting a call is: A) 0.1350.
B) 0.6065. C) 0.3935. D) 1.6490. E) 0.8650.
Q4) The selling price of various homes in a community follows the normal distribution with a mean of $176,000 and a standard deviation of $22,300.What is the probability that the next house will sell for between $150,000 and $168,000?
Q5) What does it mean when we say a random variable is standardized?
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Chapter 8: Sampling Distributions
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Sample Questions
Q1) Briefly,what is the difference between a standard deviation and a standard error?
Q2) A Poisson probability distribution with a mean of 4 must have a standard deviation of ____________________.
Q3) Assume that all possible simple random samples of size two are taken from this population,and that the original population is normally distributed.Apply the Central Limit Theorem to find the mean of the sampling distribution of sample means.
Q4) The average number of customers that visited a particular store during the past year is 160 per day and a standard deviation of 25 customers per day.A random sample of 64 days is chosen from this population.The standard deviation of the sample mean equals:
A) 12.649.
B) 25.0.
C) 2.56.
D) 3.125.
E) 8.0
Q5) Find the mean and standard deviation of the sampling distribution of the mean.
Mean = ____________________
SD = ____________________
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Chapter 9: Estimation From Sample Data
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Sample Questions
Q1) The sample variance s<sup> 2</sup> is an unbiased estimator of the population variance \(? ^ { 2 }\) when the denominator of s<sup> 2</sup> is:
A) n + 2.
B) n + 1.
C) n.
D) n - 1.
Q2) In surveying a simple random sample of 1000 assistant professors,we found that 573 of them felt they were underpaid by at least $3500.Based on these results,we have a 95% confidence that the proportion of the population of assistant professors who share this sentiment is between .548 and .598. Identify the point estimate of the population proportion.
Q3) The office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient in order to better schedule appointments.A random sample of 49 is taken and the sample mean is 20.3 minutes.Assume that the office manager knows from past experience that the standard deviation is 14 minutes.She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean? What is the confidence coefficient?
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Chapter 10: Hypothesis Tests Involving a Sample Mean or Proportion
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Sample Questions
Q1) State the null and alternative hypothesis.
Q2) State the decision rule in terms of the critical value.
Q3) What is the decision rule in terms of the sample mean \(\bar { x }\) ?
Q4) State the null and alternative hypotheses.
Q5) The ____________________ will bound rejection and non-rejection regions for the null hypothesis.
Q6) Calculate the probability of a Type II error for the following test of hypothesis H<sub>0</sub>: \(\mu\) = 50 versus H<sub>1</sub>: \(\mu\) > 50 given that \(\mu\) = 55, \(\alpha\) =.05, \(\text { }\) = 10,and n = 16.
Q7) State the null and alternative hypotheses.
Q8) For a two-tail hypothesis test,the level of significance is the sum of both tail areas. A)True B)False
Q9) What is the probability of making a Type II error if the true mean is 14?
Q10) What is the decision rule?
Page 12
Q11) What standard error will be associated with this test?
Q12) State the null and alternative hypotheses.
Q13) What is the interpretation of your conclusion?
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Chapter 11: Hypothesis Tests Involving Two Sample Means
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Sample Questions
Q1) In testing whether the means of two normal populations are equal,summary statistics computed for two independent samples are as follows: \[\begin{array} { | c | c | }
\hline \text { Brand } \boldsymbol { X } & \text { Brand } \boldsymbol { Y } \\
\hline n _ { 1 } = 25 & n _ { 2 } = 25 \\
\bar { x } _ { 1 } = 7.30 & \bar { X } _ { 2 } = 6.80 \\ s _ { 1 } = 1.05 & s _ { 2 } = 1.20 \\
\hline
\end{array}\] Assume that the population variances are equal.Then,the standard error of the sampling distribution of the sample mean difference \(\overline { \mathrm { x } } _ { 1 } - \overline { \mathrm { x } } _ { 2 }\) is equal to:
A) 0.1017.
B) 1.2713.
C) 0.3189. D) 1.1275.
Q2) What is the test statistic?
Appropriate test: ____________________
Test statistic = ____________________
Q3) Explain what the interval estimate tells you.
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Chapter 12: Analysis of Variance Tests
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Sample Questions
Q1) What decisions can be made about the null hypothesis for the main effects and the interaction effects at the 0.05 significance level?
Q2) Test for the main effects of factor A at the 5% significance level.
Q3) When there are two treatment groups,one-way ANOVA is equivalent to the pooled-variances t-test.
A)True
B)False
Q4) Compute the mean squares for treatments (MSTR).
Q5) Compute the test statistic.
Test statistic = ____________________ = ____________________
Q6) Error sum of squares
A)SST
B)SSTR
C)SSE
D)MSTR
E)MSE
Q7) Using \(\alpha\) = 0.05,state the decision rule in terms of the critical value.
Q8) What is the number of the error degrees of freedom?
Q9) In the two-way ANOVA,what is meant by the term "replications"?
Q10) What is the computed value for Factor B (music)mean square (MSB)? Page 15
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Chapter 13: Chi-Square Applications
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Sample Questions
Q1) In a goodness-of-fit chi-square test,if the null hypothesis states "The sample was drawn from a population that follows the normal distribution" and the test has 7 categories that are mutually exclusive and exhaustive,the number of degrees of freedom will be
A) 4
B) 5
C) 6
D) 7
E) 8
Q2) Find the chi-square value for each of the four degrees of freedom below,given that the area to the left of a chi-square value is 0.05.
A)2 ____________________
B)6 ____________________
C)10 ____________________
D)26 ____________________
Q3) What is the expected frequency of the 18 or more category?
Q4) What is the calculated value of the test statistic?
Q5) Test the equality of proportions at the 0.05 level the hypotheses. State the decision rule in terms of the critical value. What is the conclusion?
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Chapter 14: Nonparametric Methods
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Sample Questions
Q1) The Wilcoxon signed rank test for paired samples is used to test the hypotheses \[H _ { 0 } : m _ { d } = 0 \text { vs. } H _ { 1 } : m _ { d } \neq 0\] What is the calculated test statistic,W?
Q2) No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the calculated value of the test statistic Fr?
Q3) The sign test for comparing paired samples assumes that the measurement scale of the sample data is:
A) nominal.
B) ordinal.
C) interval.
D) ratio.
E) Any measurement scale can be used for the sign test for comparing paired samples.
Q4) On a multiple-choice exam consisting of ten questions with A through E as choices,the correct answers were: A A D A C B A D C B.Use these data to test the hypothesis that the answer sequence is random.What is the expected number of runs?
Q5) What is the rank assigned to the four observations of value 22?
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Chapter 15: Simple Linear Regression and Correlation
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Sample Questions
Q1) Construct a 95% prediction interval for an individual y value when x = 6.5.
Q2) When the predicted values of y and the actual values of y are the same,the standard error of estimate will be 0.0.
A)True
B)False
Q3) Correlation analysis provides us with two important measures of the strength: (1)the coefficient of ____________________ and (2)the coefficient of
Q4) The number of degrees of freedom associated with the standard error of estimate is
A) n-1 since only the slope is estimated from sample data.
B) n-1 since only the intercept is estimated from sample data.
C) n-1 since only the predicted value of y is estimated from sample data.
D) n-2 since the slope and the intercept are estimated from sample data.
Q5) Correlation analysis is used to determine the:
A) strength of the relationship between x and y.
B) least squares estimates of the regression parameters.
C) predicted value of y for a given value of x.
D) coefficient of determination.
Q6) Create a normal probability plot of the residuals
Page 19
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Chapter 16: Multiple Regression and Correlation
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Sample Questions
Q1) For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.
Q2) The amount of variation in the dependent variable that is not explained by the multiple regression equation is known as:
A) total sum of squares.
B) residual sum of squares.
C) regression sum of squares.
D) treatment sum of squares.
Q3) A multiple regression model has three independent variables.The following values of y and \(\hat { Y }\) are given: \[\begin{array} { | l |
| } \hline y & 40.60 & 39.40 & 38.80 & 70.60 & 49.50 &
\\ \hat { y } & 47.07 & 44.50 & 41.09 &
&
&
&
&
&
&
&
&
&
&
\end{array}\] Compute the multiple standard error of the estimate.
Q4) Calculate the coefficient of multiple determination.
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Chapter 17: Model Building
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Sample Questions
Q1) In general,on what basis are independent variables selected for entry into the equation during stepwise regression?
Q2) Consider the model described by the equation \(E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }\) .Which term provides a nonlinear component to the model allowing the line to curve?
A)\(\beta _ { 0 }\)
B)\(\beta _ { 1 } x\)
C)\(\beta _ { 2 } x ^ { 2 }\)
D)\(\beta _ { 3 } x ^ { 3 }\)
Q3) Consider the model described by the equation \[E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }\] .Which term provides a nonlinear component to the model enabling the line to reverse the direction of curvature?
A)\(\beta _ { 0 }\)
B)\(\beta _ { 1 } x\)
C)\(\beta _ { 2 } x ^ { 2 }\)
D)\(\beta _ { 3 } x ^ { 3 }\)
Q4) How do we test the reliability of a model?
Q5) What is a correlation matrix,and what role does it play in multiple regression?
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Chapter 18: Models for Time Series and Forecasting
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Sample Questions
Q1) ____________________ are measures intended to reflect the extent to which various parts of the year experience higher or lower levels of production,demand,or other kinds of economic activity.
Q2) The seasonal index is a factor that inflates or deflates a trend value to compensate for the effect of a pattern that repeats over a period of one year or less.
A)True
B)False
Q3) The estimated true value of community water consumption is 500,000 gallons for a given month.Assume that the cyclical component is 125% of normal,with seasonal and irregular components 70% and 105% of normal,respectively.Use the multiplicative time series model in determining the quantity of water consumed during the month.
Q4) If summer 2003 sales were $12,600 and the summer seasonal index was 1.20.What is the de-seasonalized 2003 summer sales value? Remove all commas from your answer before submitting.
Q5) Distinguish between the four components of a time series.Define each component.
Q6) Using a four-period moving average,what is the forecasted value for time period 5?
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Chapter 19: Decision Theory
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Sample Questions
Q1) Which of the following represents behavior of risk avoidance?
A) Bungee jumping.
B) Buying lottery tickets.
C) Entering magazine sweepstakes.
D) Buying a car with an air bag for both front seat occupants.
E) Skydiving.
Q2) Calculate the expected opportunity loss for Alternative A (in thousands of dollars). ____________________ thousand
Q3) Construct the regret matrix.
Q4) What price should ABC choose using the maximax criterion?
Q5) Calculate the expected value of perfect information (EVPI)in thousands of dollars. ____________________ thousand
Q6) The manager of a small local airport must extend a runway if business jets are to be accommodated.However,the residents living close to the airport are already complaining to the city council about the volume and noise of existing air traffic at the facility.Identify the decision alternatives and the possible states of nature that might occur after the decision is made.
Q7) Convert the payoff table to a regret table
Page 23
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Chapter 20: Total Quality Management
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Sample Questions
Q1) Much of the emphasis in TQM is on understanding and reducing variation within the process through which the product is produced,and samples of output are used in reaching inferences about the stability of the process.
A)True
B)False
Q2) A random sample of 100 rods from a process with a mean of 20 feet produced a sample mean of 20.01 feet and a standard deviation of 0.015.This difference between the process mean and the sample mean is likely to be:
A) assignable variation.
B) special-cause variation.
C) random variation.
D) homoscedasticity.
E) costs of attrition.
Q3) Identify the circumstances when the \(\bar{x}\) chart and R chart might be useful.
Q4) In terms of random variation and assignable variation,what is meant by the statement,"The process is in control"?
Q5) What is a quality audit,and for what purposes might one be performed?
Q6) What is a control chart,and what purpose does it serve?
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