Quantitative Methods for Business Final Exam
Course Introduction
Quantitative Methods for Business introduces students to the analytical tools and techniques used to solve business problems and inform decision-making. The course covers topics such as descriptive statistics, probability distributions, sampling methods, hypothesis testing, regression analysis, and linear programming. Through a blend of theory and practical application, students learn to collect, analyze, and interpret quantitative data, and use statistical software to support business decisions in areas such as operations, marketing, finance, and management. Emphasis is placed on developing critical thinking and problem-solving skills essential for effective business analysis in a data-driven environment.
Recommended Textbook
Essentials of Business Statistics 1st Canadian Edition by Ken Black
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Chapter 1: Introduction to Statistics
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Sample Questions
Q1) Which of the following statements is correct?
A) Business researchers rarely give attention to collecting meaningful data.
B) Variables are data that can be directly used for decision making.
C) Valid data are the lifeblood of business statistics.
D) Measurements never need to be defined by the business researcher.
E) Business statistics are extremely complex and hard to use for decision making.
Answer: C
Q2) Miguel Hernandez, Senior Vice President of Human Resources at Memorial Hospital, is exploring the usage of nursing over-time hours in the emergency department during the last operating year (January 1, 2012, through December 31, 2012). Miguel intends to survey the emergency department nurses regarding their perception of over-time needs. For this survey y the set of all emergency department nurses who worked at Memorial Hospital during the last operating year is ___.
A) a parameter
B) a sample
C) the population
D) a statistic
E) the frame
Answer: C
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Chapter 2: Organizing and Visualizing Data
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Sample Questions
Q1) The difference between the highest number and the lowest number in a set of data is called the differential frequency.
A)True
B)False
Answer: False
Q2) A scatter plot is a two-dimensional graph plot of data containing pairs of observations on two numerical variables.
A)True
B)False
Answer: True
Q3) A scatter plot shows how the numbers in a data set are scattered around their average.
A)True
B)False
Answer: False
Q4) A cumulative frequency polygon is also called an ogive.
A)True
B)False Answer: True
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Chapter 3: Descriptive Statistics
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Sample Questions
Q1) When you use Excel's most powerful statistical tools, the results
A) update automatically when you change the data.
B) are static.
C) can only be run for one statistical test at a time.
D) are temporary.
Answer: B
Q2) The number of speeding tickets given by a sample of 14 police officers in a month are as follows: 63, 35, 67, 63, 55, 75, 84, 13, 67, 54, 59, 49, 58, and 67. Compute the range, interquartile range and the standard deviation.
Answer: Range = 71, Interquartile range (IQR) = 13, Standard deviation = 17.36
Q3) A nonzero value of the skewness indicates asymmetry of the distribution of the data.
A)True
B)False
Answer: True
Q4) Skewness indicates that a data distribution is symmetrical or asymmetrical.
A)True
B)False
Answer: True
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Page 5
Chapter 4: Gathering Data
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Sample
Questions
Q1) A carload of palletized aluminum castings has arrived at Mansfield Motor Manufacturers. The car contains 1,000 pallets of 100 castings each. Mario Munoz, manager of Quality Assurance, directs the receiving crew to deliver the 127th and 869th pallets to his crew for 100% inspection. Mario randomly selected 127 and 869 from a table of random numbers. Mario's sample of 200 castings is a ___.
A) simple random sample
B) systematic sample
C) stratified sample
D) cluster sample
E) convenience sample
Q2) Which one of the following is \(\textbf{ not }\) a reason for taking a sample instead of conducting a census?
A) The sample can save money.
B) The sample can save time.
C) The population is difficult to access.
D) The safety of the consumer.
E) none of the above
Q3) What is the difference between a census and a sample?
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Chapter 5: Probability
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Sample Questions
Q1) If E and F are mutually exclusive, then ___.
A) the probability of the union is zero
B) P(E) = 1 - P(F)
C) the probability of the intersection is zero
D) the probability of the union is one
E) P(E) = P(F)
Q2) If two events are mutually exclusive, then the two events are also independent. A)True
B)False
Q3) Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. Find probability that the student is enrolled in either finance or in statistics or both.
Q4) The list of all elementary events for an experiment is called the sample space. A)True
B)False
Q5) What are the three methods of assigning probabilities?
Q6) Name the branch of statistics that is supported by probability.
Page 7
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Chapter 6: Decision Analysis and Expected Value
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Sample Questions
Q1) The variance of a discrete distribution increases if we add a positive constant to each one of its value.
A)True B)False
Q2) The number of visitors to a website each day is an example of a discrete random variable.
A)True B)False
Q3) In a decision-making scenario, if the decision maker knows which state of nature will occur, the scenario is called decision-making under certainty.
A)True B)False
Q4) The value of perfect information is the difference between the monetary payoff with perfect information and the expected monetary payoff with no information.
A)True B)False
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Chapter 7: Discrete Probability Distributions
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Sample Questions
Q1) Suppose X has a geometric distribution with probability 0.3 of success on each observation. The probability that X is 4 is
A) 0.0081.
B) 0.0189.
C) 0.1029.
D) 0.2401.
E) 0.2409.
Q2) For the Poisson distribution the mean represents twice the value of the standard deviation.
A)True
B)False
Q3) Aluminum castings are processed in lots of five each. A sample of two castings is randomly selected from each lot for inspection. A particular lot contains one defective casting; and x is the number of defective castings in the sample. P(x=1) is ___.
A) 0.2
B) 0.4
C) 0.6
D) 0.8
E) 1.0
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Chapter 8: Continuous Distributions
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Q1) Since a normal distribution curve extends from minus infinity to plus infinity, the area under the curve is infinity.
A)True
B)False
Q2) If x is continuously uniformly distributed over the interval 8 to 12, inclusively (8 \(\le\) x \(\le\) 12), then the probability, P(10.0 \(\le\) x \(\le\) 11.5), is ___.
A) 0.250
B) 0.333
C) 0.375
D) 0.500
E) 0.750
Q3) The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.
A)True
B)False
Q4) Suppose x is uniformly distributed over some interval and the mean value ( ) of x is 2 and its variance ( <sup>2</sup>) is 1/3. Find the probability that x is between 2 and 2.5, P(2 \(\le\) x \(\le\) 2.5).
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Chapter 9: Sampling Distributions
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Sample Questions
Q1) Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is ___.
A) 0.9974
B) 0.4987
C) 0.9772
D) 0.4772
E) 0.5000
Q2) If the population is normally distributed, the sample means of a sample of size n = 5 are normally distributed.
A)True
B)False
Q3) Let x be a binomial random variable with n = 50 and ? = 0.3. Determine the probability of at most 13 successes, using the normal approximation for binomial distribution.
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Chapter 10: Confidence Intervals
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Sample Questions
Q1) Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using ___.
A) a point estimate
B) a range estimate
C) a statistical parameter
D) an interval estimate
E) an exact estimate
Q2) The table t value associated with the upper 5% of the t distribution and 14 degrees of freedom is ___.
A) 2.977
B) 2.624
C) 2.145
D) 1.761
E) 1.345
Q3) A sample of 120 adults from a large population has a mean IQ of 112 with a standard deviation of 10. Construct a 98% confidence interval for the true mean IQ of the population.
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Chapter 11: Hypothesis Testing for Single Populations
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Q1) A researcher is testing a hypothesis of a single mean. The critical z value for \(\alpha\) =.05 and a two-tailed test is ±1.96. The observed z value from sample data is 2.85. The decision made by the researcher based on this information is to ___ the null hypothesis.
A) reject
B) not reject
C) redefine
D) change the alternate hypothesis into E) restate the null hypothesis
Q2) In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is \(\textbf{ not }\) known, which of the following statistical test should be used?
A) z test of a population mean
B) t test of a population mean
C) z test of a population proportion
D) \(\chi\)<sup>2</sup> test of a population variance
E) t test of a population proportion
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Chapter 12: Hypothesis Testing for Two Populations
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Sample Questions
Q1) A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors. This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule. To test this theory the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week. A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week. A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week. The observed z for this is ___.
A) 0.300
B) 0.624
C) 0.638
D) 11.22
E) 13.42
Q2) The difference in two sample means is normally distributed for sample sizes 30, only if the populations are normally distributed.
A)True
B)False
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Chapter 13: Analysis of Variance Anova
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Sample Questions
Q1) The statistical methods of analysis of variance assume equal sample means.
A)True
B)False
Q2) As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Your null hypothesis is ___.
A)
\(\mu\)<sub>1</sub>\(\neq\)\(\mu\)<sub>2</sub>\(\neq\)\(\mu\)<sub>3</sub>
B) \(\mu\)<sub>1</sub> \(\ge\)\(\mu\)<sub>2</sub> \(\ge\) \(\mu\)<sub>3</sub>
C) \(\mu\)<sub>1</sub>\(\le\) \(\mu\)<sub>2</sub> \(\le\)\(\mu\)<sub>3</sub>
D)\(\mu\)<sub>1</sub>=\(\mu\)<sub>2</sub>=\(\mu\)<sub>3</sub>
E) \(\mu\)<sub>1</sub>\(\le\) \(\mu\)<sub>2</sub> \(\ge\)\(\mu\)<sub>3</sub>
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Chapter 14: Linear Correlation and Simple Linear Regression Analysis
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Q1) In regression, the variable that is being predicted is usually referred to as the independent variable.
A)True
B)False
Q2) One of the assumptions made in simple regression is that ___.
A) the error terms are normally distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are all equal
Q3) A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The dependent variable is ___.
A) day of week
B) production run
C) percentage of defects
D) number of defects
E) number of production runs
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Chapter 15: Categorical Versus Categorical: Tests
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Q1) A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using \(\alpha\)=.01, the observed value of chi-square is ___. A) 12.09
13.28
Q2) A two-way table used for a test of independence is sometimes called a contingency table.
A)True
B)False
Q3) In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.
A)True B)False
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