Decision Making with Statistics
Exam Questions
Course Introduction
This course explores the principles and techniques of statistical analysis as they apply to effective decision making in various fields such as business, healthcare, and public policy. Students will learn how to collect, interpret, and analyze data using statistical tools and models, understand the importance of probability in assessing risk, and apply inferential statistics to solve real-world problems. Emphasis is placed on translating statistical results into actionable insights, making informed choices amidst uncertainty, and critically evaluating the quality of data-driven decisions. Real-life case studies and hands-on projects will provide practical application of key concepts throughout the course.
Recommended Textbook
Business Statistics in Practice 3rd Canadian Edition by Bruce L. Bowerman
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2568 Verified Questions
2568 Flashcards
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Chapter 1: An Introduction to Business Statistics
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Sample Questions
Q1) In situations when it is not possible to number all of the units in a population,we often use a _____ sample to approximate a random sample.
Answer: systematic
Q2) A consumer's yes/no reply to a survey question is what type of variable?
Answer: qualitative
Q3) Temperature, (in degrees Celsius)is an example of a(n)________ variable.
A)nominative
B)ordinal
C)interval
D)ratio
E)random
Answer: C
Q4) Statistical inference is the science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.
A)True
B)False
Answer: True
Q5) A _____ is an examination of all the population measurements.
Answer: census
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Chapter 2: Descriptive Statistics
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Sample Questions
Q1) Personnel managers usually want to know where a job applicant ranked in an entrance test for their company.With a score of 3.83,Michelle Robinson ranked above the 93<sup>rd</sup> percentile of the other applicants.What is the percentile rank of an applicant whose score was the median value?
Answer: 50<sup>th</sup>
Q2) What is the 10<sup>th</sup> percentile?
Answer: D
Q3) What is the variance? A)18 B)4.73 C)22.40 D)324
E)6.76
Answer: C
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Page 4
Chapter 3: Probability
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Sample Questions
Q1) Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E | A)= .10,P(E | B)= .05,and P(E | C)= 0.What is P(B | E)?
Answer: 1818 \[\begin{array} { l }
P ( B \cap E ) = ( .20 ) ( .05 ) = .01 \\
P ( E ) = ( .45 ) ( .10 ) + ( .20 ) ( .05 ) + ( .35 ) ( 0 ) = .055 \\
P ( B \mid E ) = \frac { P ( B \cap E ) } { P ( E ) } = \frac { .01 } { .055 } = .1818 \end{array}\]
Q2) What is the probability a customer neither buys beer nor buys cigars?
Answer: .95 \[\begin{array} { l }
P ( \text { Beer } ) = \frac { P ( \text { Beer } \cap \text { Cigar } ) } { P ( \text { Beer } \mid \text { Cigar } ) } = \frac { .01 } { .25 } = .04 \\
P ( \text { No Cigar } \cap \text { Beer } ) = .03 \\
P ( \text { No Cigar } \cap \text { No Beer } ) = .98 - .03 = .95 \end{array}\]
Q3) A(n)______________ is a collection of sample space outcomes.
Answer: Event
Q4) D and C
Answer: Yes
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Page 5
Chapter 4: Discrete Random Variables
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Sample Questions
Q1) When using hypergeometric distribution,it is assumed that the trials are __________ and the probability of success ________ from trial to trial.
A)independent,does not change
B)dependent,does not change
C)independent,changes
D)dependent,changes
Q2) Exactly three of the individuals has type A blood?
Q3) Find the standard deviation of X.
Q4) 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
Q5) Compute the expected value of X.
Q6) Find the expected value of X.
Q7) What is the probability that of the 20 invoices written,five or more would contain errors if the theory is valid?
6
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Chapter 5: Continuous Random Variables
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Sample Questions
Q1) Find P(X < 6).
Q2) If the random variable of x is normally distributed,____ % of all possible observed values of x will be within two standard deviations of the mean.
Q3) If the random variable of x is normally distributed,68.26% of all possible observed values of x will be within two standard deviations of the mean.
A)True
B)False
Q4) Given that X is a normal random variable,the probability that a given value of X is below its mean is ________________.
Q5) The specific shape of each normal distribution is determined by its _____ and _____.
Q6) What price will 77% of the drink prices fall above?
Q7) What is the standard deviation of the temperature increase?
Q8) What proportion of tests has scores over 90?
Q9) Find z when the area to the left of z is .05
Q10) What is the probability that a standard normal random variable will be between -2 and 2?
Page 7
Q11) What percentage of students scored between 81 and 89?
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Chapter 6: Sampling Distributions
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Sample Questions
Q1) The notation for the standard deviation of the sample mean is also known as the standard __________.
Q2) Suppose you take a sample of size 4 from a population with a mean of 70 and a standard deviation of 10.Based on such a sample,what are the mean and standard deviation of the sampling distribution of \(\bar { x }\) ?
A) \(\mu _ { \bar { x } }\) = 70, \(\sigma _ { \bar { x } }\) = 5
B) \(\mu _ { \bar { x } }\) = 70, \(\mu _ { \bar { x } }\) = 2.5
C) \(\mu _ { \bar { x } }\) = 17.5, \(\mu _ { \bar { x } }\) = 5
D) \(\mu _ { \bar { x } }\) = 17.5, \(\mu _ { \bar { x } }\) = 10
E)Cannot be determined unless the sample size is at least 30.
Q3) If we take a sample of any size from a population with mean \(\mu\) and standard deviation \(\sigma\) ,then the standard deviation of the sampling distribution of the sample mean \(\bar { x }\) is \(\sigma\) .
A)True
B)False
Q4) The spread of the sampling distribution of \(\bar { x }\) is ____________ than the spread of the corresponding population distribution.
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Chapter 7: Confidence Intervals
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Sample Questions
Q1) The appropriate hypotheses to test the advertising department's claim is _____.
A)H<sub>0</sub>: p .365 vs H<sub>A</sub>: p > .365
B)H<sub>0</sub>: p .250 vs H<sub>A</sub>: p < .250
C)H<sub>0</sub>: p .250 vs H<sub>A</sub>: p > .250
D)H<sub>0</sub>: p = .250 vs H<sub>A</sub>: p .250
E)H<sub>0</sub>: p .250 vs H<sub>A</sub>: p = .250
Q2) When testing the difference between two population proportions using large,independent random samples,the appropriate test statistic is based on the ____ distribution.
A)z
B)t
C)F
D)chi-square
E)exponential
Q3) Write the alternative hypothesis.
Q4) Write the null hypothesis.
Q5) The _____ hypothesis will be accepted only if there is convincing sample evidence that it is true.
Q6) What is the decision at \(\alpha\) = 0.05?
Q7) What is the decision at \(\alpha\) = 0.10?
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Chapter 8: Hypothesis Testing
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Sample Questions
Q1) Suppose we are comparing two population means from normally distributed populations based on independent random samples and unknown,but equal,population variances.If n<sub>1</sub> = 13 and n<sub>2</sub> = 10,then degrees of freedom for the t statistic is 22.
A)True
B)False
Q2) The null and alternative hypotheses for the possibility that sodium levels are higher than the manufacturer's claims is _____.
A)H<sub>0</sub>: ? = 471 vs.H<sub>a</sub>: ? ? 471
B)H<sub>0</sub>: ? ? 471 vs.H<sub>a</sub>: ? < 471
C)H<sub>0</sub>: ? ? 174 vs.H<sub>a</sub>: ? < 174
D)H<sub>0</sub>: ? ? 471 vs.H<sub>a</sub>: ? = 471
E)H<sub>0</sub>: ? ? 471 vs.H<sub>a</sub>: ? > 471
Q3) In testing the difference between population variances of two normally distributed populations using independent random samples,the F statistic can assume either a positive or a negative value.
A)True
B)False
Q4) What is the decision at alpha = .05?
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Chapter 9: Statistical Inferences Based on Two Samples
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Sample Questions
Q1) In general,replacing a z with a t when using a preliminary sample to obtain an estimate of the variance is a _____ decision.
Q2) A 93% confidence interval for \(\mu\) ,the mean number of days of sick leave would be _____.
A)[10.725,13.675]
B)[10.390,14.010]
C)[12.019,12.381]
D)[12.053,12.348]
E)[11.735,12.665]
Q3) In a survey of 400 people,60 percent favour new zoning laws.Find a 95 percent confidence interval for the true proportion favouring new laws.
Q4) What is a 95 percent confidence interval for \(\mu\) when n = 10, \(\bar { x }\) = 34.1,and s = 3.0? Assume population normality.
Q5) Calculate a 90 percent confidence interval for \(\mu\) .
Q6) What is a 95 percent confidence interval for \(\mu\) when n = 10, \(\bar { x }\) = 35.6,and s = 13.0? Assume population normality.
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Chapter 10: Experimental Design and Analysis of Variance
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Sample Questions
Q1) Find Tukey's simultaneous 95 percent confidence interval for \(\mu _ { 1 } - \mu _ { 2 }\) where \(\bar { x } _ { 1 }\) = 51.5, \(\bar { x } _ { 2 }\) = 55.8,and MSE = 6.125.There were 4 treatments and 24 observations in total and the number of observations were equal in each group.
Q2) What is the between-groups mean square?
Q3) Complete the ANOVA table and calculate F.
Q4) Test HS1U1B10S1U1B0: there is no difference between effects of levels of factor II at a =.05.
Q5) In an experiment,the response variable is also known as the _______ variable.
Q6) What is the total sum of squares?
Q7) The 95% individual confidence interval for \(\mu _ { 1 } - \mu _ { 2 }\) will always be narrower than the Tukey 95% simultaneous confidence interval for \(\mu _ { 1 } - \mu _ { 2 }\) . A)True B)False
Q8) What is the degrees of freedom for blocks?
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Chapter 11: Correlation Coefficient and Simple Linear
Regression Analysis
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Sample Questions
Q1) Write the equation of the least squares line.
Q2) The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
A)True
B)False
Q3) What is the value of SSxy?
A)7.368
B)8.748
C)1.844
D)4.745
E)5.140
Q4) Calculate the coefficient of determination.
Q5) Determine the 95% prediction interval for the mean value of y when x = 35 Givens: x = 277 and x<sup>2</sup> = 8705
Q6) Find the rejection point for the t statistic at a = .05 and test H<sub>0</sub>: ?<sub>1</sub>= 0 vs.H<sub>a</sub>: b<sub>1</sub>¹ 0.
Q7) Find the estimated y-intercept.
Q8) Calculate the SSE
Q9) Calculate the standard error. Page 13
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Chapter 12: Multiple Regression and Model Building
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Sample Questions
Q1) Test the overall usefulness of the model at ? = .01.Calculate F and make your decision.
Q2) Calculate the proportion of the variation explained by the multiple regression model.
Q3) Below is a partially completed multiple regression analysis of variance (ANOVA)table.Calculate R<sup>2</sup>.
Q4) A fitted multiple regression model yields an R<sup>2</sup> of 0.64.Interpret this value.
A)64% of the independent variables used in the regression model are highly correlated and may falsely suggest a curvilinear relationship exists between x and y when the true relationship is linear.
B)64% of the variation in the observed value of the dependent variable is explained by the regression model.
C)The correlation between each pair of independent variables is 0.8 or -0.8.
D)The fitted model predicts the dependent variable accurately 64% of the time.
E)64% of the independent variables in the model are capable of accurately predicting the dependent variable.
Q5) Calculate the adjusted R<sup>2</sup>.
Q6) What is the mean square error?
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Chapter 13: Nonparametric Methods
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Sample Questions
Q1) The Wilcoxon rank sum test is used to compares the locations of two _____________ populations.
Q2) State the null and alternative hypotheses to test the claim.Assume that the population of selling prices is not normally distributed.
Q3) Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?
A)Wilcoxon signed rank test
B)Sign test
C)Kruskall-Wallis test
D)Wilcoxon rank sum test
E)Spearman's test
Q4) Assume that the population of starting salaries in marketing is not normally distributed.The p-value is found to be .0547.Using a = .10,can we conclude that the starting salaries have increased in the last five years?
Q5) Calculate the value of T<sub>i</sub> (rank sum)for each of the three samples.
Q6) What is the test statistic T?
Q7) What is the rejection point T<sub>0</sub> for \(\alpha\) = .05?
Q8) State the null and alternative hypotheses.
Page 16
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Chapter 14: Chi-Square Tests
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Sample Questions
Q1) The <sup>2</sup> statistic from a contingency table with 6 rows and 5 columns will have:
A)30 degrees of freedom
B)24 degrees of freedom
C)5 degrees of freedom
D)20 degrees of freedom
E)25 degrees of freedom
Q2) The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is _____.
Q3) In performing a chi-square goodness fit test for a normal distribution,a researcher wants to make sure that all of the expected cell frequencies are at least five.The sample is divided into 7 intervals.The second through the sixth interval all have expected cell frequencies of at least five.The first and the last intervals have expected cell frequencies of 1.5 each.After adjusting the number of intervals,the degrees of freedom for the chi-square statistic is ____.
Q4) Calculate the chi-square statistic for this test of independence.
Q5) The <sup>2</sup> goodness of fit test requires nominative level of data.
A)True
B)False
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Chapter 15: Decision Theory
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Sample Questions
Q1) The _____________________ criterion is attractive to those decision-makers who exhibit a neutral approach towards decision choices involving risk.
A)expected utility
B)expected monetary value
C)maximin
D)maximax
E)decision theory
Q2) A person's utility is determined by the preferences they exhibit for decision choices involving __________.
A)certainty
B)uncertainty
C)risk
D)Bayes' Theorem
E)optimism
Q3) A corn farmer has categorized the weather into three possible levels.The weather conditions will affect the timing of the harvest and the associated payoff.In this situation,the weather conditions are called the ____________________________.
Q4) Which investment would the investor select if the maximax criterion is used?
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Chapter 16: Time Series Forecasting
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Sample Questions
Q1) Calculate the mean squared deviation (MSD)for Model 1.
Q2) 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
Q3) When there is first-order autocorrelation,the error term in period t is related to the error term in period ______.
Q4) Compute the Paasche index for 2011.
A)101.68
B)112.67
C)105.46
D)108.41
E)100
Q5) A positive autocorrelation implies that negative error terms will be followed by _________ error terms.
Q6) Compute the total forecast error (sum of the forecast errors)
Q7) Consider the following set of quarterly sales data given in thousands of dollars.
Q8) Weighting in exponential smoothing is accomplished by the use of a _____.
Page 19
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