Quantitative Methods for Business Solved Exam Questions
Course Introduction
Quantitative Methods for Business introduces students to the fundamental mathematical and statistical techniques used in business decision-making. Topics covered include data analysis, probability, sampling, hypothesis testing, regression analysis, linear programming, and forecasting. Through practical applications and real-world case studies, students will learn how to apply quantitative tools to solve business problems, interpret results, and make informed managerial decisions. This course emphasizes analytical thinking and provides essential skills for further study in finance, marketing, operations, and management.
Recommended Textbook
Statistical Techniques in Business and Economics 15th Edition by Douglas A. Lind
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Chapter 1: What Is Statistics
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Sample Questions
Q1) The general process of gathering, organizing, summarizing, analyzing, and interpreting data is called
A) Statistics.
B) Descriptive statistics.
C) Inferential statistics.
D) Levels of measurement.
Answer: A
Q2) A scale used to measure a quantitative variable is either _______________ or ______________.
Answer: interval, ratio
Q3) Data measured on a nominal scale can only be classified into categories.
A)True
B)False
Answer: True
Q4) The principal difference between the interval and ratio scale of measurement is that the ratio scale has a __________________.
Answer: meaningful zero point
Q5) Ranked data is an example of what level of measurement? ________________
Answer: Ordinal
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Sample Questions
Q1) What is the number of observations in each class of a frequency distribution called?
Answer: Class frequency or frequency
Q2) The midpoint of a class interval is also called a class __________.
Answer: mark
Q3) A ______ chart is useful for displaying a relative frequency distribution. Answer: Pie
Q4) A _____ chart is useful for displaying a frequency distribution for a qualitative variable.
Answer: bar
Q5) In frequency distributions, classes are mutually exclusive if each individual, object, or measurement is included in only one category.
A)True
B)False
Answer: True
Q6) In constructing a frequency polygon, class frequencies are scaled on which axis?
Answer: Y or vertical axis
4
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) The standard deviation is the positive square root of the variance.
A)True
B)False
Answer: True
Q2) For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.
A)True
B)False
Answer: False
Q3) If the variance of the "number of daily parking tickets issued" is 100, the variance is defined as
A) "number of daily parking tickets".
B) "number of daily parking tickets" squared.
C) the absolute value of the "number of daily parking tickets".
D) the square root of the "number of daily parking tickets".
Answer: B
Q4) Which measure of central location requires that the data be ranked before it is possible to determine it? ____________
Answer: Median
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Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) In a distribution, the second quartile corresponds with the A) Mean.
B) Median.
C) Mode.
D) Variance.
Q2) The lengths of stay on the cancer floor of Community Hospital were organized into a frequency distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The standard deviation was computed to be 4.2 days. What is the Pearson's coefficient of skewness? __________
Q3) The "box" in a box plot shows the interquartile range.
A)True
B)False
Q4) A sample of experienced typists revealed that their mean typing speed is 87 words per minute and the median is 73. The standard deviation is 16.9 words per minute. What is the Pearson's coefficient of skewness?
A) -2.5
B) -4.2
C) +4.2
D) +2.5
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Chapter 5: A Survey of Probability Concepts
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Sample Questions
Q1) A graphical method used to calculate joint and conditional probabilities is A) a tree diagram.
B) a Venn diagram.
C) a histogram.
D) inferential statistics.
Q2) What is the probability that a flipped coin will show heads on four consecutive flips?
Q3) When an experiment is conducted "without replacement,"
A) events are dependent
B) events are equally likely
C) the experiment can be illustrated with a Venn Diagram
D) the probability of two or more events is computed as a joint probability
Q4) In flipping a fair coin, what is the probability of a head and a tail on one toss?
Q5) Complete the following analogy: an experiment relates to outcome, as the role of a die relates to _____.
Q6) When the special rule of multiplication is used, the events must be
Q7) In flipping a fair coin, what is the probability of either a head or a tail on one toss?
Page 7
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) When observing a check-out line at a food store, the average number of people served is 30 per hour. Using the Poisson distribution, what is the probability that no (zero) people check out in any given hour?
Q2) For any probability distribution, the mean is calculated as a weighted mean. The weights are the ______________.
Q3) A continuous random variable can assume one of an ____________ number of values within a specific range.
Q4) When sampling is done without replacement and the outcomes are measured as either a success or failure, the hypergeometric distribution should be applied. A)True
B)False
Q5) A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
A) 0
B) 0.016
C) 0.062
D) 0.250
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Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) What proportion of the area under a normal curve is to the right of a z-score of zero?
Q2) The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the area under the normal curve between 400 and 482?
A) 0.5000
B) 0.4495
C) 0.3413
D) 0.4750
Q3) The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?
A) 60.06%
B) 39.94%
C) 34.13%
D) 81.66%
Q4) In a standard normal distribution, µ = ______ and \(\sigma\) = _____.
Q5) To apply the normal approximation to a binomial distribution, mean and variance are ________
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) A population consists of 12 values. How many samples of size six are possible?
Q2) The central limit theorem allows us to use a z-statistic to compute probabilities for the sampling distribution of the sample mean.
A)True
B)False
Q3) A university has 1000 computers available for students to use. Each computer has a 250 gigabyte hard drive. The university wants to estimate the space occupied on the hard drives. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the probability that a sample mean is between 111 and 119 gigabytes?
Q4) When testing the safety of cars using crash tests, a sample of 1 or 2 cars is used because
A) Sampling is more accurate.
B) Cars are destroyed.
C) It is quicker.
D) The population is very large.
Q5) Sampling from a population may be preferred because studying all the items in a population may be too ____________.
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Q6) A population consists of 14 values. How many samples of size five are possible?
Chapter 9: Estimation and Confidence Intervals
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Sample Questions
Q1) In terms of the standard error of the mean, how wide is a 99 percent confidence interval? ______
Q2) When a confidence interval for a population mean is constructed from sample data, A) we can conclude that the population mean is in the interval B) we can conclude that the population mean is not in the interval C) we can conclude, for an infinite number of samples and corresponding confidence intervals, that the population mean is in a stated percentage of the intervals D) we cannot make any inferences
Q3) What does the t distribution approach as the sample size increases?
Q4) A company wants to estimate next years total revenue. Why is an interval estimate preferred to a point estimate?
Q5) To compute a confidence interval, a __________ is used when the population standard deviation is known.
Q6) A point estimate is a single value used to estimate a population parameter. A)True B)False
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Chapter 10: One-Sample Tests of Hypothesis
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Sample Questions
Q1) A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want to buy a condominium in Florida. What is the test statistic to evaluate the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium?
Q2) Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is \(\pi\) = 0.55 and the alternate is \(\pi\) \(\neq\).55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?
A) Do not reject it
B) Reject it
C) Cannot accept nor reject it based on the information given D) Purchase a condominium.
Q3) A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.222 and a standard deviation of 1.2019. At the 0.025 significance level, what is the critical value?
Q4) When planning an experiment, how is a significance level related to sample size?
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Chapter 11: Two-Sample Tests of Hypothesis
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Sample Questions
Q1) If two dependent samples of size 20 are used to test the difference between the means, the degrees of freedom for a t-statistic are 19.
A)True
B)False
Q2) A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds?
What is the computed value of the test statistic? ______________
Q3) If the null hypothesis states that there is no difference between the two population means, then the test is ______________.
Q4) The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.
A)True
B)False
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Chapter 12: Analysis of Variance
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Sample Questions
Q1) In a two-way ANOVA, the sources of variation are
A) Total variation and error variation.
B) Total variation, treatment variation, and error variation.
C) Total variation, treatment variation, blocking variation and error variation.
D) Treatment variation and blocking variation.
Q2) What statistical technique is used to test the equality of three or more population means? ____________________
Q3) In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the numerator? ______
Q4) In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the sum of squares for the error is 0.09, what is the mean square for the error? ______
Q5) When testing a hypothesis regarding the equality of two population means, what is the analogy to a blocking variable?
Q6) How many mean square errors are summarized in a two-way ANOVA table?
Q7) The F distribution is a ______________ distribution.
Q8) What is the shape of the F distribution? ______________________
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Chapter 13: Correlation and Linear Regression
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Sample Questions
Q1) What is the purpose of measuring correlation?
Q2) Select a value for the correlation coefficient and provide a complete interpretation of the correlation coefficient using your selected value.
Q3) A chart that shows the relationship between a dependent variable and an independent variable is called a ______________________.
Q4) The regression equation is = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope?
A) z = -4.364
B) z = 4.364
C) t = -4.364
D) t = -0.96
Q5) If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?
A) Not related
B) Dependent on each other
C) Highly related
D) X causes Y
Q6) What are the inputs and the output of linear regression?
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Chapter 14: Multiple Regression Analysis
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Sample Questions
Q1) How are residual plots drawn and used to evaluate the assumptions of linear multiple regression?
Q2) In an ANOVA table for a multiple regression analysis, total variation is separated into
A) treatment and error variation
B) regression and residual variation
C) treatment and block variation
D) block and error variation
Q3) In multiple regression analysis, what scale is used to measure a dummy variable?
Q4) What statistic is used to assess multicollinearity in multiple regression analysis?
Q5) A researcher is studying the effect of ten different variables on a critical measure of business performance. What method can be used to select the best set of variables to predict performance?
A) Stepwise Regression.
B) ANOVA.
C) Simple linear regression.
D) Residual analysis.
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Chapter 15: Index Numbers
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Sample Questions
Q1) In a weighted index, what variable is usually the weight?
Q2) The 2001 CPI was 171.1 (1982-84=100). What is the purchasing power of the dollar relative to the base?
Q3) Which method of computing index numbers has the advantage that the consumption pattern is always up-to-date? _____________________
Q4) The CPI for "personal computers and peripheral equipment" in June 2006 was 10.7 (1982-1984 = 100). Interpret this index.
A) There was no significant increase in the price of "personal computers and peripheral equipment"
B) The price of "personal computers and peripheral equipment" increased 10.7%.
C) The price of "personal computers and peripheral equipment" decreased 89.3%.
D) If the average price of a computer in 1982-1984 was $3000.00, the CPI for "personal computers and peripheral equipment" would predict that the price of a computer in June 2006 would be $893.
Q5) In 2000, an executive earned $100,000. In 2010, the executive earned $125,000. The CPI in 2000 was 172.2; the CPI in 2009 was 214.537. Using the CPI base, 1982-1984 = 100, what was the real income in 2000?
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Chapter 16: Time Series and Forecasting
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Sample Questions
Q1) For a five-year moving average, how many values will be lost at the beginning and end of the time series?
A) 0 at the start and 4 at the end
B) 3 at the start and 3 at the end
C) 2 at the start and 2 at the end
D) 0 at the start and 5 at the end
Q2) A useful method for smoothing a time series to examine trend is called a ______.
Q3) A graph of a deseasonalized time series does NOT show ________.
Q4) The trend forecast equation is = 120+ 100t. The next forecast is for period 11. The typical seasonal index for period 11 is 0.82. What are the forecast sales for period 11?
A) 1,100
B) 1,220
C) 1,000
D) 640
Q5) Why are long range predictions considered essential to managing a firm?
A) To develop plans for possible new plants
B) To have raw materials available for future demand
C) To develop plans for future financing
D) All of the above
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Chapter 17: Nonparametric Methods: Goodness-Of-Fit
Tests
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Sample Questions
Q1) If we wanted to see if tossing a die (a cube with the sides numbered one through six) had an equal chance of showing each side or number, what statistical test should be applied?
Q2) Nonparametric tests require no assumptions about the shape of the population distribution.
A)True
B)False
Q3) For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are
A) linear.
B) curvilinear.
C) not related.
D) related.
Q4) What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?
A) Do not reject the null hypothesis
B) Reject the null hypothesis
C) Unable to reject or not reject the null hypothesis based on data
D) Should take a larger sample
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Chapter 18: Nonparametric Methods: Analysis of Ranked
Data
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Sample Questions
Q1) The Spearman coefficient of rank correlation requires that observations be _______.
Q2) What is a null hypothesis for a one-tail sign test?
A) H<sub>0</sub>: \(\pi\) = 0
B) H<sub>0</sub>: \(\pi\) \(\le\)1.00
C) H<sub>0</sub>: \(\pi\) = 0.50
D) H<sub>0</sub>:\(\pi\) \(\le\) 0.50
Q3) 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The test statistic is:
A) 0.707
B) 1.179
C) 1.707
D) 0.179
Q4) The _____________ of the differences between "before and after" measurements is evaluated in a Wilcoxon Signed-Rank test.
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Q5) The Wilcoxon signed-rank test requires the populations to be _____________.
Chapter 19: Statistical Process Control and Quality Management
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Sample Questions
Q1) A sampling plan states that if 20 incoming bolts are checked and 2 or less defective bolts are discovered the lot will be rejected. If an incoming lot is 10 percent defective, what is the probability of rejecting the lot?
A) 0
B) 1
C) 0.323
D) 0.667
Q2) A Pareto chart is useful because it is based on the theory that 80% of the observations are accounted for by 20% of the ________.
Q3) A fishbone diagram starts with the definition of a problem and explores its possible ________.
Q4) What is the purpose of quality control in production and service operations?
Q5) In acceptance sampling, there is one unique operating characteristic curve for a specified sampling plan.
A)True
B)False
Q6) A fishbone diagram is an ________________ tool.
Q8) Explain the risks of acceptance sampling. Page 21
Q7) The measurement of color is an _____________.
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Chapter 20: An Introduction to Decision Theory
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Q1) What is the difference between the expected monetary value under conditions of certainty and the expected monetary value under uncertainty called? ___________
Q2) In statistical decision making, the act or decision alternative yielding the maximum expected payoff also yields the minimum ________________.
Q3) Sensitivity analysis examines the effects that changes in the probabilities for the states of nature have on the expected values of the alternatives or acts, and the corresponding decisions.
A)True
B)False
Q4) When all the facts are known in a decision-making situation, it can be said that the decision was made under conditions of _____________.
Q5) A table to organize decision-making data, including various acts and possible profits or losses, is called a _______________________.
Q6) What is the potential loss associated with a future state of nature called?
Q7) The maximin strategy is a __________ strategy for decision making.
Q8) A decision-maker selects a course of action called an ________________.
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