Statistical Methods for Economics and Business Practice Exam
Course Introduction
This course provides an introduction to statistical techniques commonly applied in economics and business settings. Students learn foundational concepts in probability, data collection, and data presentation, progressing to more advanced topics such as estimation, hypothesis testing, regression analysis, and forecasting. Emphasis is placed on interpreting results and applying quantitative reasoning to real-world economic and business problems. Practical experience with statistical software enables students to analyze actual datasets, equipping them with essential decision-making tools for the professional environment.
Recommended Textbook
Business Statistics in Practice 3rd Canadian Edition by Bruce L. Bowerman
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Page 2
Chapter 1: An Introduction to Business Statistics
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Sample Questions
Q1) Any characteristic of a population unit is a(n):
A)measurement
B)sample
C)observation
D)variable
E)trait
Answer: D
Q2) _____ is the science of describing the important aspects of a set of measurements.
Answer: Descriptive statistics
Q3) A consumer's yes/no reply to a survey question is what type of variable?
Answer: qualitative
Q4) When a population unit selected as part of the sample cannot be contacted or refuses to participate,then we say that _________ has occurred.
Answer: nonresponse
Q5) The process of assigning a value of a variable to each unit in a population or sample is called _____.
Answer: measurement
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Chapter 2: Descriptive Statistics
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Sample Questions
Q1) Calculate a two standard deviation tolerance interval for the data that has a sample mean of 28,475 and a standard deviation of 9,369.
Answer: 9,737 to 47,213
28,475 - 2(9,369)= 9,737
28,475 + 2(9,369)= 47,213
Q2) What is the smallest percent spent on computing?
A)5.9
B)5.6
C)5.2
D)5.02
E)50.2
Answer: C
Q3) What are three important properties of any data set?
Answer: central tendency,variation,and shape
Q4) A measurement located between the inner and outer fences of a box-and-whisker display is a(n)_____.
Answer: mild outlier
Q5) Determine the sample mean of the data 5,4,8,6,1,0,2,6.
Answer: 4
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Chapter 3: Probability
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Sample Questions
Q1) What is the probability that one randomly selected undergraduate will be either a female or belong to a Greek organization?
Answer: 73%
P(G \(\cup\)
F)= .55 + .25 - .07 = .73
Q2) Probabilities must be assigned to experimental outcomes so that the probabilities of all the experimental outcomes must add up to ___.
Answer: 1
Q3) What is the probability of winning four games in a row,if the probability of winning each individual game is 1/2,independent of each other game?
A)1/4
B)1/6
C)1/8
D)1/12
E)1/16
Answer: E
Q4) If you roll a fair die,what is the probability that at least 5 dots appear?
Answer: 1/3 \[\frac { 2 } { 6 }\]
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Chapter 4: Discrete Random Variables
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Sample Questions
Q1) What is the probability that during the next five minutes three cars will arrive?
Q2) A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5)will occur less than 3 times?
A)0547
B)1172
C)1550
D)7752
E)8450
Q3) According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?
A)0002
B)0243
C)0378
D)0467
E)0697
Q4) If 100 calculators are selected at random,what is the expected number of defectives?
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Chapter 5: Continuous Random Variables
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Sample Questions
Q1) Find P(X < 12).
Q2) Beyond age 85
Q3) A normal population has a mean of 10 and a variance of 4.What is P(X < 6)?
A)0.0228
B)0.4772
C)0.0398
D)0.0438
E)0.4948
Q4) A normal population has a mean of 10 and a variance of 4.What is P(X > 7)?
A)0.6844
B)0.9987
C)0.8913
D)0.7750
E)0.9332
Q5) The weight of a product is normally distributed with a standard deviation of .5 grams.What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 grams?
Q6) At least 10 minutes
Q7) The specific shape of each normal distribution is determined by its _____ and _____.
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Chapter 6: Sampling Distributions
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Sample Questions
Q1) If a sample size is at least _____,then for any sampled population,we can conclude that the sample means are approximately normal.
Q2) Suppose you take a random sample of size n = 4 from a normally distributed population with \(\mu\) = 16 and \(\sigma\) = 8.Find P( \(\bar { x }\) < 25).
Q3) Find P(\(\hat { p }\) > .175).
Q4) If p = .9 and n = 40,then we can conclude that the sampling distribution of \(\hat { p }\) is approximately a normal distribution.
A)True B)False
Q5) The sampling distribution of the sample mean is approximately normal for sufficiently ________ sample sizes regardless of the distribution shape of the sampled population.
Q6) Suppose you take a random sample of size n = 16 from a normally distributed population with \(\mu\) = 40 and \(\sigma\) = 16.Find P( \(\bar { x }\) < 35).
Q7) Suppose you take a random sample of size n = 100 from a population with \(\mu\) = 400.If P( \(\bar { x }\) < 380)= 0.0668,find \(\sigma\) .
Q8) Find P( \(\hat { p }\) < .18).
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Chapter 7: Confidence Intervals
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Sample Questions
Q1) Write the alternative hypothesis.
Q2) Test H<sub>0</sub>: \(\mu\) \(\geq\)
22 versus H<sub>a</sub>: \(\mu\) < 22,given \(\alpha\) = .01,n = 100, \(\bar { x }\) = 21.431,and \(\alpha\) = 1.295.
Reject H<sub>0</sub><sub> </sub><sub> </sub><sub> </sub> <sub> </sub>
Q3) When conducting a hypothesis test about a population mean,other relevant factors held constant,increasing the level of significance from .05 to .10 will reduce the probability of a Type I error.
A)True
B)False
Q4) A researcher wishes to test H<sub>0</sub>:
Q5) What is the decision at \(\alpha\) = 0.01?
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Chapter 8: Hypothesis Testing
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Sample Questions
Q1) Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. H<sub>A</sub>: ?<sub>A</sub> > ?<sub>B</sub>, \(\bar { X }\) <sub>1</sub> = 12, \(\bar { X }\) <sub>2</sub> = 9,s<sub>1</sub> = 5,s<sub>2</sub> = 3,n<sub>1</sub> = 13,n<sub>2</sub> = 10.
A)t = 1.677
B)t = 1.5
C)t = 2.823
D)t = 1.674
E)t = 1.063
Q2) What is the F-statistic for testing H<sub>0</sub>: <sub>1</sub><sup>2</sup> <sub>2</sub><sup>2</sup>,H<sub>A</sub>: <sub>2</sub><sup>2</sup> > <sub>1</sub><sup>2</sup> at = .05 where n<sub>1</sub> = 16,n<sub>2</sub> = 19,s<sub>1</sub><sup>2</sup> = .03,s<sub>2</sub><sup>2</sup> = .02.
Q3) Test H<sub>0</sub>: 3.0 versus H<sub>A</sub>: > 3.0 when
Q4) Test H<sub>0</sub>: = 32 versus H<sub>A</sub>: > 32 when
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Chapter 9: Statistical Inferences Based on Two Samples
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Sample Questions
Q1) Recently,a case of food poisoning was traced to a particular restaurant chain.The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur.Despite the response from the restaurant chain,many consumers refused to visit the restaurant for some time after the event.What sample size would be needed in order to be 95% confident that the sample proportion is within 0.02 of p,the true proportion of customers who refuse to go back to the restaurant?
A)14
B)38
C)129
D)2401
E)1,777
Q2) In a survey of 308 adults,17 listed jewellery among the romantic gifts men want to receive.The 98% confidence interval for the proportion of all adults who include jewellery among their responses would be _____.
A)[.025,.085]
B)[.169,.171]
C)[.120,.220]
D)[.140,.200]
E)[.050,.170]
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Page 11
Chapter 10: Experimental Design and Analysis of Variance
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Sample Questions
Q1) Suppose that a teacher wants to study how four different study methods affect a student's final grade.The study method is the _____ variable.
A)biased
B)response
C)random
D)unknown
E)independent
Q2) Consider the following one-way ANOVA table. \[\begin{array} { l c c }
\text { Source } & \text { d.f. } & \text { Sum of Squares } \\ \text { Model } & 3 & 213.88125 \\
\text { Error } & 20 & 11.208333 \\
\text { Total } & 23 & 225.0895
\end{array}\]
What is the value of the F statistic for testing for a difference between group means?
Q3) Find Tukey's simultaneous 95 percent confidence interval for the difference between the means of block 2 and block 4.
Q4) What is the degrees of freedom for factor I?
Q5) What is the calculated F statistic for blocks?
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Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Sample Questions
Q1) The least-squares point estimates of the simple linear regression model minimize the _____.
Q2) Use the least squares regression equation,
Q3) The sample correlation coefficient may assume any value between:
A)0 and 1
B)-× and ×
C)0 and 8
D)-1 and 1
E)-1 and 0
Q4) The least-squares regression line is the line that minimizes:
A)the explained variation
B)SSyy
C)total variation
D)SSxx
E)SSE
Q5) The ____________________ is the proportion of the total variation in the dependent variable explained by the regression model.
Q6) Provide an interpretation of the estimated slope.
Q7) Find the estimated slope.
13
Q8) Provide an interpretation of the slope estimate.
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Chapter 12: Multiple Regression and Model Building
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Sample Questions
Q1) In the quadratic regression model y = ?<sub>0</sub>+ ?<sub>1</sub>x + ?<sub>2</sub>x<sup>2</sup>+ ?,if the value of the term ?<sub>1</sub>increases,then the parabola shifts to the _________.
Q2) The general form of the quadratic multiple regression models is:
A)y = \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub>+ \(\varepsilon\)
B)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub>+ \(\varepsilon\)
C)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X + \(\beta\) <sub> </sub> <sub>2</sub>X<sup>2</sup>+ \(\varepsilon\)
D)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sup>2</sup>+ \(\varepsilon\)
E)y = \(\beta\) <sub> </sub> <sub>0</sub>+ \(\beta\) <sub> </sub> <sub>1</sub>X<sub>1</sub>+ \(\beta\) <sub> </sub> <sub>2</sub>X<sub>2</sub><sup>2</sup>+ \(\varepsilon\)
Q3) Determine the degrees of freedom regression (explained variation),degrees of freedom error (unexplained variation),and total degrees of freedom for the model with two independent variables.
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Chapter 13: Nonparametric Methods
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Sample Questions
Q1) Two professional football scouts are in the process of recruiting 7 new football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.The rankings are given below.
Q2) Which of the following statements about nonparametric methods is correct?
A)Nonparametric methods are only used in cases where parametric tests such as t or F do not exist.
B)Nonparametric tests should always be used when one is available because they are easier to apply then their parametric counterparts.
C)Nonparametric tests are useful alternatives to parametric tests such as t or F when certain assumptions required by parametric tests are violated.
D)Nonparametric tests are only used if the data comes from independent samples.
E)Nonparametric tests cannot be used if the same value appears in more than one data set being analyzed.
Q3) State the null and alternative hypotheses to test the claim.Assume that the population of selling prices is not normally distributed.
Q4) At \(\alpha\) = .05,test to determine if the protocol increases test scores.
Q5) What is the appropriate null and alternative hypothesis for this problem?
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Chapter 14: Chi-Square Tests
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Sample Questions
Q1) When we carry out a chi-square test of independence,the expected frequencies are based on the null hypothesis.
A)True
B)False
Q2) At a significance level of 0.05,determine the appropriate degrees of freedom and the rejection point condition for the test.
Q3) Calculate the value of the chi-square statistic.
Q4) At a significance level of .05,what is the appropriate rejection point condition?
A)Reject H<sub>0</sub> if ?<sup>2</sup> > 12.5916
B)Reject H<sub>0</sub> if ?<sup>2</sup> > 11.0705
C)Reject H<sub>0</sub> if ?<sup>2</sup> > 9.3484
D)Reject H<sub>0</sub> if ?<sup>2</sup> > 7.81473
E)Reject H<sub>0</sub> if ?<sup>2</sup> > 9.48773
Q5) How many degrees of freedom are associated with the chi-square test?
Q6) A contingency table summarizes data that has been classified on two dimensions or scales.
A)True B)False
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Chapter 15: Decision Theory
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Sample Questions
Q1) A tire manufacturer needs to make a decision about the amount of production for the coming month (high vs.low).The level of production largely depends on the level of demand.For this situation,the levels of demand (high,medium,low)represent alternatives.
A)True
B)False
Q2) Maximax is a criterion used when making decisions under __________________.
A)certainty
B)uncertainty
C)risk
D)alternatives
Q3) The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.
A)True
B)False
Q4) The maximin criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.
A)True
B)False
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Chapter 16: Time Series Forecasting
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Sample Questions
Q1) Compute the Laspeyres index for 2011.
A)100
B)101.73
C)108.91
D)105.62
E)114.11
Q2) A major drawback of the aggregate price index is that:
A)It does not take into account the fact that some items in the market basket are purchased more frequently than others.
B)It is difficult to compute.
C)It is computed by using the values from a single time series or based on a single product.
D)Percentage comparisons cannot be made to the base year.
Q3) Weighting in exponential smoothing is accomplished by the use of a _____.
Q4) Holt-Winters' double exponential smoothing would be an appropriate method to use to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns.
A)True
B)False
Q5) Compute the Paasche index using 1990 as the base year.
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