Business Statistics
Midterm Exam
Course Introduction
Business Statistics is a foundational course that introduces students to the concepts and methods of statistical analysis within a business context. The course covers topics such as data collection, descriptive statistics, probability distributions, hypothesis testing, regression analysis, and quality control. Emphasizing practical application, students learn to interpret data, make informed decisions, and solve real-world business problems using statistical tools and software. By the end of the course, students are equipped with the analytical skills needed to evaluate business strategies, assess risk, and contribute to data-driven decision-making in various organizational settings.
Recommended Textbook
Business Statistics For Contemporary Decision Making 9th Edition by Ken Black
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Chapter 1: Introduction to Statistics
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Q1) Statistics is commonly divided into two branches called descriptive statistics and summary statistics.
A)True
B)False
Answer: False
Q2) You are the owner of a camping site and want to estimate the level of customer satisfaction among your clients.For this purpose,you select a representative sample of your clients and offer them a discount good for their next visit as compensation for filling out a short questionnaire.One question specifically says,"How satisfied are you with your experience,on a scale from (1)to (5),where (1)is 'very dissatisfied' and (5)is 'very satisfied'?" This is an example of _______.
A) interval level data
B) ordinal level data
C) nominal level data
D) ratio level data
E) relative level data
Answer: B
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Chapter 2: Charts and Graphs
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Sample Questions
Q1) Dot Plots are mainly used to display a large data set.
A)True
B)False
Answer: False
Q2) The staffs of the accounting and the quality control departments rated their respective supervisor's leadership style as either (1)authoritarian or (2)participatory.
Sixty-eight percent of the accounting staff rated their supervisor "authoritarian," and thirty-two percent rated him "participatory." Forty percent of the quality control staff rated their supervisor "authoritarian," and sixty percent rated her "participatory." The best graphic depiction of these data would be two ___________________.
A) histograms
B) frequency polygons
C) ogives
D) pie charts
E) scatter plots
Answer: D
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4
Chapter 3: Descriptive Statistics
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Sample Questions
Q1) An electrical component for one of the main products your company produces is specified to have an electrical impedance of 2.15 ohms.However,the manufacturing process is not perfect and there is some variation on the actual impedance of these components.A recent statistical study indicated that in fact,the impedances are normally distributed with a mean impedance of 2.15 ohms and a standard deviation of 0.05 ohms.When the impedance exceeds 2.25 ohms,the product malfunctions so that component must be rejected and replaced by one whose impedance is within the acceptable limit.If you need 1350 usable components,how many components should you order?
A) 1608
B) 1422
C) 1421
D) 1385
E) 1384
Answer: D
Q2) If the median of a distribution is greater than mean,then the distribution is skewed to the left.
A)True
B)False
Answer: True
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Page 5
Chapter 4: Probability
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Q1) If two events are mutually exclusive,then the two events are also independent.
A)True
B)False
Q2) Given two events,A and B,if the probability of either A or B occurring is 0.6,then the probability of neither A nor B occurring is -0.6.
A)True
B)False
Q3) An event that cannot be broken down into other events is called a certainty outcome.
A)True
B)False
Q4) The department in which you work in your company has 10 employees: 10 women and 14 men.A team of anywhere from one employee up to 9 employees must be chose to attend a meeting at the company's headquarters.How many different teams can be selected?
A) 1024
B) 1023
C) 1022
D) 1021
E) 1020
Page 6
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Chapter 5: Discrete Distributions
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Sample Questions
Q1) One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample,x has a _______________ distribution.
A) continuous
B) normal
C) binomial
D) hypergeometric
E) exponential
Q2) Which of the following conditions is not a condition for the hypergeometric distribution?
A) the probability of success is the same on each trial
B) sampling is done without replacement
C) there are only two possible outcomes
D) trials are dependent
E) n < 5%N
Q3) In a hypergeometric distribution the population,N,is finite and known.
A)True
B)False
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Page 7
Chapter 6: Continuous Distributions
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Sample Questions
Q1) If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140,inclusively (90 \(\le\) x \(\le\) 140),then the standard deviation of this distribution is __________________.
A) 4.16
B) 50
C) 14.4
D) 7.07
E) 28.2
Q2) Let z be a normal random variable with mean 0 and standard deviation 1.The 90<sup>th</sup> percentile of z is ____________.
A) 1.645
B) -1.254
C) 1.960
D) 1.280
E) 1.650
Q3) The normal approximation for binomial distribution can be used when n=10 and p=1/5.
A)True
B)False
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Page 8
Chapter 7: Sampling and Sampling Distributions
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Q1) Suppose 40% of the population of pre-teens have a TV in their bedroom.If a random sample of 500 pre-teens is drawn from the population,then the probability that 44% or more of the pre-teens have a TV in their bedroom is _______.
A) 0.9644
B) 0.4644
C) 0.0356
D) 0.0400
E) 0.9600
Q2) Catherine Chao,Director of Marketing Research,needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package,the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is
A) 0.9232
B) 0.0768
C) 0.4616
D) 0.0384
E) 0.8974
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Chapter 8: Statistical Inference: Estimation for Single Populations
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Sample Questions
Q1) The z value associated with a two?sided 80% confidence interval is _______.
A) 1.645
B) 1.28
C) 0.84
D) 0.29
E) 2.00
Q2) Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package. She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages; she will accept a 0.05 error. Previous studies indicate that new packaging has an approximately 70% acceptance rate.The sample size should be at least _______.
A) 27
B) 59
C) 323
D) 427
E) 500
Q3) A t-distribution is similar to a normal distribution,but with flatter tails.
A)True
B)False
Page 10
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Chapter 9: Statistical Inference: Hypothesis Testing for
Single Populations
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Sample Questions
Q1) In performing hypothesis tests about the population mean,if the population standard deviation is not known,a t test can be used to test the mean if _________________.
A) n is small
B) the sample is random
C) the population mean is known
D) the population is normally distributed
E) the population is chi-square distributed
Q2) When a false null hypothesis is rejected,the researcher has made a Type II error. A)True
B)False
Q3) The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.
A)True
B)False
Q4) A z test of proportions is used when a hypothesis test is conducted on a population proportion.
A)True B)False
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Chapter 10: Statistical Inferences About Two Populations
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Q1) To determine if there is a difference in the speed of a wireless router from two different manufacturers a network manager will draw independent samples of wireless routers from the two manufacturers and compare the difference in the sample means for the connection speed.
A)True
B)False
Q2) Hypothesis tests conducted on sets of matched samples are sometimes referred to as correlated t tests.
A)True
B)False
Q3) The F statistic is a ratio of two independent sample variances.
A)True
B)False
Q4) When finding a confidence interval for the difference between two population proportions we use the pooled estimate of the proportion.
A)True
B)False
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12
Chapter 11: A Nalysis of Variance and Design of Experiments
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Q1) Cindy Ho,VP of Finance at Discrete Components,Inc.(DCI),theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly,she has designed an experiment to test her theory using four sales discount rates (0%,2%,4%,and 6%). First,she classified DCI's credit customers into three categories by total assets (small,medium,and large). Then,she randomly assigned four customers from each category to a sales discount rate. Cindy's null hypothesis is ________.
A) \(\mu\)<sub>1</sub>\(\neq\)\(\mu\)<sub>2</sub> \(\neq\)\(\mu\)<sub>3</sub>\(\neq\)\(\mu\)<sub>4</sub>
B) \(\mu\)<sub>1</sub> \(\ge\)\(\mu\)<sub>2</sub> \(\ge\) \(\mu\)<sub>3</sub>\(\ge\) \(\mu\)<sub>4</sub>
C) \(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub> = \(\mu\)<sub>3</sub>=\(\mu\)<sub>4</sub>
D) \(\mu\)<sub>1</sub> \(\le\)\(\mu\)<sub>2</sub> \(\le\) \(\mu\)<sub>3</sub>\(\le\) \(\mu\)<sub>4</sub> E)\(\mu\)<sub>1</sub> \(\le\)\(\mu\)<sub>2</sub> \(\ge\) \(\mu\)<sub>3</sub>\(\le\) \(\mu\)<sub>4</sub>
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Chapter 12: Simple Regression Analysis and Correlation
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Sample Questions
Q1) In a simple regression the coefficient of correlation is the square root of the coefficient of determination.
A)True
B)False
Q2) The difference between the actual y value and the predicted y value found using a regression equation is called the residual.
A)True
B)False
Q3) If x and y in a regression model are totally unrelated,_______.
A) the correlation coefficient would be -1
B) the coefficient of determination would be 0
C) the coefficient of determination would be 1
D) the SSE would be 0
E) the MSE would be 0s
Q4) The assumptions underlying simple regression analysis include ______________.
A) the error terms are exponentially distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are independent
Chapter 13: Multiple Regression Analysis
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Q1) A human resources analyst is developing a regression model to predict electricity production plant manager compensation as a function of production capacity of the plant,number of employees at the plant,and plant technology (coal,oil,and nuclear).The "plant technology" variable in this model is ______.
A) a response variable
B) a dependent variable
C) a quantitative variable
D) an independent variable
E) a constant
Q2) In the multiple regression model y = \(\beta\)<sub> 0</sub> + \(\beta\)<sub> 1</sub>x<sub>1</sub> + \(\beta\)<sub> 2</sub>x<sub>2</sub> + \(\beta\)<sub> 3</sub>x<sub>3</sub> + \(\varepsilon\),the \(\beta\) coefficients of the x variables are called partial regression coefficients.
A)True
B)False
Q3) Multiple t-tests are used to determine whether the independent variables in the regression model are significant.
A)True
B)False
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Chapter 14: Building Multiple Regression Models
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Q1) A research project was conducted to study the effect of a chemical on undesired insects.The researcher uses 6 dose levels,and at each level exposes 250 insects to the chemical and proceeds to count the number of insects that die.The researcher uses a binary logistic regression model to estimate the probability of death as a function of dose. Shown below is Minitab output from a logistic regression. Coefficients
Term Coef SE Coef 95% CI Z-Value P-Value VIF
Constant -2.644 0.156 (-2.950,-2.338) -16.94 0.000
Dose 0.6740 0.0391 (0.5973,0.7506) 17.23 0.000 1.00
Odd Ratios for Continuous Predictors
Odds Ratio 95% CI
Dose 1.9621 (1.8173,2.1184)
The estimated odds of death at a given level divided by the estimated odds of death at the following level equals = ______.
A) 1.9621
B) 0.6470
C) 0.5097
D) 0.3271
E) 0.3008
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Chapter 15: Time-Series Forecasting and Index Numbers
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Sample Questions
Q1) If autocorrelation occurs in regression analysis,then the confidence intervals and tests using the t and F distributions are no longer strictly applicable.
A)True
B)False
Q2) Which of the following is not a component of time series data?
A) Trend
B) Seasonal fluctuations
C) Cyclical fluctuations
D) Normal fluctuations
E) Irregular fluctuations
Q3) If the Year<sub>t</sub> Quarter<sub>q</sub> actual value is 9,885 and the corresponding Year<sub>t</sub> Quarter<sub>q</sub> seasonal index is 97.75,then the Year<sub>t</sub> Quarter<sub>q</sub> deseasonalized value is ______.
A) 222.41
B) 9,662.59
C) 9,775.00
D) 10,083.18
E) 10,112.53
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Chapter 16: Analysis of Categorical Data
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Q1) The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one.
A)True
B)False
Q2) A cancer research group surveys 100 women more than 40 years old to test the hypothesis that 50% of women in this age group have regularly scheduled mammograms.Forty of the women respond affirmatively.Using \(\alpha\) = 0.05,the appropriate decision is ________.
A) do not reject the null hypothesis p 0.50
B) reject the null hypothesis p = 0.50
C) reject the null hypothesis p < 0.50
D) p < 0.50
E) do nothing
Q3) In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 7.
A)True
B)False
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Chapter 17: Nonparametric Statistics
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Q1) Suppose a research uses the Mann-Whitney test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study. If,among all 17,the sum of the ranks W<sub>1</sub> produced from the rural high school students is 72,the U statistic is
A) 29
B) 45
C) 90
D) 36
E) 43
Q2) The nonparametric alternative to analysis of variance for a randomized block design is the Friedman test.
A)True
B)False
Q3) In the one-sample runs test for randomness of the observations in a large sample the sampling distribution of R,the number of runs,is approximately binomial.
A)True
B)False
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Page 19
Chapter 18: Statistical Quality Control
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Sample Questions
Q1) Inspecting the attributes of a finished product to determine whether the product is acceptable,is in need of rework,or is to be rejected is called after-process quality control.
A)True
B)False
Q2) Two general types of control charts are (1)control charts for measurements and (2)control charts for compliance items.
A)True
B)False
Q3) A company that uses benchmarking as a quality improvement practice will
A) emulate the best practices and techniques used in their industry
B) institutionalize the not-invented-here philosophy
C) not analyze the competition's product
D) rely exclusively on government research for product improvements
E) be in the furniture business
Q4) The Six Sigma approach essentially calls for the process to approach defect-free status.
A)True B)False
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Chapter 19: Decision Analysis
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Sample Questions
Q1) Dan Hein owns the mineral and drilling rights to a 1,000 acre tract of land. If he drills a well and does not strike oil his net loss will be $50,000,but if he drills a well and strikes oil his net gain will be $100,000.If he does not drill,his loss is the cost of the mineral and drilling rights,which amount to $1000.For Dan's decision problem,the variable "drill the well" is one of the ___________.
A) payoffs
B) decision alternatives
C) states of nature
D) revised probabilities
E) prior probabilities
Q2) In a decision-making under uncertainty scenario,the decision maker chooses the decision alternative that has the minimum expected (i.e.,probability-weighted)payoff among all the available alternatives.
A)True
B)False
Q3) The expected monetary payoff of perfect information is the value of perfect information.
A)True
B)False
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Page 21