Business Statistics
Final Exam
Course Introduction
Business Statistics introduces students to the fundamental concepts and methods of statistical analysis as applied to business decision-making. The course covers topics such as descriptive statistics, probability distributions, sampling techniques, estimation, hypothesis testing, regression analysis, and forecasting. Emphasis is placed on the practical application of statistical tools to real-world business problems, enabling students to interpret data, draw meaningful conclusions, and make data-driven decisions. Throughout the course, students will also gain proficiency in using statistical software to analyze and visualize business data.
Recommended Textbook
Stats Data and Models 1st Canadian Edition by Richard D. De Veaux
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32 Chapters
1925 Verified Questions
1925 Flashcards
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Page 2
Chapter 1: Data
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Sample Questions
Q1) A person's gender
A)Quantitative
B)Categorical
Answer: B
Q2) A biologist studying hatchery fish released into rivers recorded several characteristics including length (centimetres),weight (kilograms),and life span.
A)Length,quantitative,centimetres;life span,quantitative,years.
B)Length,quantitative,centimetres;weight,quantitative,kilograms.
C)Length,quantitative,inches;weight,quantitative,pounds;life span,quantitative,years.
D)Length,quantitative,centimetres;weight,quantitative,kilograms;life span,quantitative,years.
E)Length,quantitative,inches;weight,quantitative,kilograms;life span,categorical.
Answer: D
Q3) A person's political affiliation
A)Categorical
B)Quantitative
Answer: A
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3
Chapter 2: Displaying and Describing Categorical Data
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Sample Questions
Q1) Of the 1,470 applicants to a college program,760 were accepted,269 were wait-listed,and 441 were turned away for lack of space.Find the relative frequency distribution of the decisions made,and write a sentence describing it.
A)1,470 students applied for admission to the college program.52% were accepted,18% were wait-listed,and 30% were turned away.
B)1,470 students applied for admission to the college program.52% were accepted,and 48% were turned away.
C)1,470 students applied for admission to the college program.52% were accepted,35% were wait-listed,and 30% were turned away.
D)1,470 students applied for admission to the college program.52% were accepted,35% were wait-listed,and 58% were turned away.
E)1,470 students applied for admission to the college program.70% were accepted,and 30% were turned away.
Answer: A
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4
Chapter 3: Displaying and Summarizing Quantitative Data
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Sample Questions
Q1) A small company employs a supervisor at $1,400 a week,an inventory manager at $800 a week,8 stock boys at $300 a week each,and 6 drivers at $700 a week each.
A)$2,200
B)$733
C)$500
D)$300
E)$550
Answer: E
Q2) A small company employs a supervisor at $1,300 a week,an inventory manager at $600 a week,5 stock boys at $300 a week each,and 3 drivers at $500 a week each.
A)$300
B)$500
C)$400
D)$600
E)$490
Answer: C
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Chapter 4: Understanding and Comparing Distributions
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Sample Questions
Q1) How would you describe the shape of each distribution?
A)Class1: left-skewed,spread out ranging from about 40 to 90
Class 2: left-skewed,spread out ranging from about 40 to 90
Class 3: symmetric,spread out ranging from about 40 to 90
B)Class1: fairly symmetric,spread out ranging from about 40 to 90
Class 2: left-skewed,spread out ranging from about 40 to 90
Class 3: asymmetric,spread out ranging from about 40 to 90
C)Class1: left-skewed,spread out ranging from about 40 to 90
Class 2: right-skewed,spread out ranging from about 40 to 90
Class 3: symmetric,spread out ranging from about 40 to 90
D)Class1: fairly symmetric,spread out ranging from about 40 to 90
Class 2: left-skewed,spread out ranging from about 40 to 90
Class 3: symmetric,spread out ranging from about 40 to 90
E)Class1: fairly symmetric,spread out ranging from about 40 to 90
Class 2: right-skewed,spread out ranging from about 40 to 90
Class 3: symmetric,spread out ranging from about 40 to 90
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6
Chapter 5: The Standard Deviation As a Ruler and the Normal Model
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Sample Questions
Q1) After increased patrol,cars on a road travel at speeds averaging 54 km/h.If 10% of vehicles travel above 70 km/h,what approximate standard deviation could represent this model (assuming a Normal model is appropriate)?
A)35.94
B)12.50
C)7
D)5.4
E)-12.50
Q2) Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000,mean salary = $35,000,median = $25,000,range = $60,000,IQR = $30,000,first quartile = $17,500,standard deviation = $20,000. Between what two values are the middle 50% of the salaries found?
A)$15,000 and $75,000
B)$17,500 and $37,500
C)$17,500 and $30,000
D)$35,000 and $25,000
E)$17,500 and $47,500
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Chapter 6: Scatterplots, association, and Correlation
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Sample Questions
Q1) A study is conducted on insects growth based on hydrometry.The correlation found between insects growth and hydrometry is 0.05.A journalist concludes that a low correlation between insects growth and hydrometry shows that insects can reproduce easily in a dry climate.Do you agree with this interpretation?
A)No: the correlation must be negative.
B)Yes: the correlation is close to 0.
C)Yes: the two variables are quantitative.
D)No: the relation must be linear.
E)Yes: the relation is linear.
Q2) A study is conducted on the causes of flat feet,and shows a linear relation between age and having mechanical disturbances of the foot.The correlation between these two variables is 0.84.The report concludes that older people have greater chances to have flat feet.Is the calculation of the correlation appropriate?
A)No: having mechanical disturbances of the foot is a categorical variable.
B)Yes: the two variables are quantitative.
C)No: having mechanical disturbances of the foot is a response variable.
D)Yes: correlation is less than 1.
E)Yes: age is a quantitative variable.
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Chapter 7: Linear Regression
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Sample Questions
Q1) The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression to predict the average attendance from the number of games won has an r = 0.79.Interpret this statistic.
A)Negative,fairly strong linear relationship.62.41% of the variation in average attendance is explained by the number of games won.
B)Negative,weak linear relationship.4.41% of the variation in average attendance is explained by the number of games won.
C)Positive,weak linear relationship.4.41% of the variation in average attendance is explained by the number of games won.
D)Positive,fairly strong linear relationship.79% of the variation in average attendance is explained by the number of games won.
E)Positive,fairly strong linear relationship.62.41% of the variation in average attendance is explained by the number of games won.
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Chapter 8: Regression Wisdom
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Sample Questions
Q1) An economist noticed that nations with more TV sets have higher life expectancy.He established a strong positive association between length of life and number of TV sets.Describe three different possible cause-and-effect relationships that might be present.
A)Perhaps more TV sets cause higher life expectancy,higher life expectancy cause more TV sets,or both could be caused by a lurking variable such as the wealth of the nation.
B)There is only one cause-and-effect relationship: more TV sets cause higher life expectancy.
C)Perhaps more TV sets cause higher life expectancy,higher life expectancy cause more TV sets,or both could be caused by a lurking variable such as the TV sets brand.
D)There is only one cause-and-effect relationship: higher life expectancy cause more TV sets.
E)There are only two cause-and-effect relationships: more TV sets cause higher life expectancy,or higher life expectancy cause more TV sets.
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Chapter
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Sample Questions
Q1) The relationship between two quantities x and y is examined.The relationship appears to be fairly linear.A linear model is considered,and the regression analysis is as follows:
Dependent variable: y
R-squared = 87.9%
VARIABLE COEFFICIENT
Intercept 37.74
X -9.97
What does the slope say about the relationship between x and y?
A)For each increase in x of 1,the corresponding average decrease in y is 9.97.
B)For each increase in x of 1,the corresponding average increase in y is 37.74.
C)For each increase in x of 1,the corresponding average decrease in y is 37.74.
D)For each increase in x of 1,the corresponding average increase in y is 9.97.
E)For each increase in x of 1,y decreases by and average of 87.9%.
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Chapter 10: Understanding Randomness
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Sample Questions
Q1) When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe the response variable.
A)The response variable is whether the hand had a royal flush or a full house.
B)The response variable is whether the hand had a full house.
C)The response variable is whether the hand had a neither a royal flush nor a full house.
D)The response variable is whether the hand had a royal flush.
E)The response variable is whether the hand had a royal flush,a full house,or neither.
Q2) What is the minimum number of times that an ordinary deck of playing cards must be shuffled to make the deck random?
A)7
B)1
C)2
D)8
E)It cannot be made random.
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Page 12
Chapter 11: Sample Surveys
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Sample Questions
Q1) At the local university a survey was being done on whether or not the students liked the cafeteria food.The survey was located in the college newspaper and was to be filled out and sent to the editing office.Identify the type of sampling used in this example.
A)Attempted census
B)Systematic sampling
C)Stratified sampling
D)Cluster sampling
E)Voluntary response sampling
Q2) The human resources department of a large,well-known telecommunications firm would like to know the job satisfaction of the employees working at its company,but the HR department is restricted by company policy to use only email to distribute and collect any type of employee questionnaire or survey.What sampling method is HR being forced to rely upon?
A)Stratified sampling
B)Convenience sampling
C)Voluntary response sampling
D)Attempted census
E)Cluster sampling
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Chapter 12: Experiments and Observational Surveys
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Sample Questions
Q1) Explain the difference between an observational study and an experiment.
Q2) An educational researcher used school records to determine that,in one school district,84% of children living in two-parent homes graduated high school while 75% of children living in single-parent homes graduated high school.
A)Prospective observational study
B)Retrospective observational study
C)Experiment
Q3) A manufacturer of tennis rackets has designed a new racket and would like to compare it to their previous design.Suggest an appropriate experiment.
Q4) In an experiment,explain the difference between the treatments and the factors.
Q5) Among a group of men who were tracked for ten years,those who had scored over 130 on intelligence tests were more likely to suffer severe depression than those who had scored below 130 on intelligence tests.
A)Experiment
B)Retrospective observational study
C)Prospective observational study
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14
Chapter 13: From Randomness to Probability
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Sample Questions
Q1) Toss a coin five times;record the number of heads.
A){0,1,2,3,4,5},equally likely
B){0,1,2,3,4,5},not equally likely
C){1,2,3,4,5},equally likely
D){1,2,3,4,5},not equally likely
E){1,2},equally likely
Q2) Melissa is looking for the perfect man.She claims that of the men at her college,36% are smart,26% are funny,and 13% are both smart and funny.If Melissa is right,what is the probability that a man chosen at random from her college is neither funny nor smart?
A)0
B)0.87
C)0.64
D)0.51
E)0.38
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15
Chapter 14: Probability Rules
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Sample Questions
Q1) Among the contestants in a competition are 50 women and 29 men.If 5 winners are randomly selected,what is the probability that they are all men? Round your answer to five decimal places.
A)0.01256
B)0.05605
C)0.00527
D)0.10156
E)0.06564
Q2) You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a spade given that it is not a diamond.
A)0.333
B)0.077
C)0
D)0.5
E)0.25
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Chapter 15: Random Variables
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Sample Questions
Q1) You pick a card from a deck.If you get a club,you win $80.If not,you get to draw again (after replacing the first card).If you get a club the second time,you win $30.If not,you lose.Find the standard deviation of the amount you will win.
A)$1,112.11
B)$38.07
C)$30.68
D)$28.35
E)$33.35
Q2) Miguel buys a large bottle and a small bottle of juice.The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1,018 ml and a standard deviation of 9 ml.The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 506 ml and a standard deviation of 3 ml.Find the mean and standard deviation of the total amount of juice in the two bottles.
A) = 1,524 ml, = 9.49 ml
B) = 1,136.82 ml, = 9.49 ml
C) = 1,524 ml, = 12 ml
D) = 512 ml, = 12 ml
E) = 1,524 ml, = 90 ml
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Page 17
Chapter 16: Probability Models
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Sample Questions
Q1) Suppose that 14% of people are left handed.If 8 people are picked at random,what's the probability that the first lefty is the 8th person chosen?
A)0.1400
B)0.0419
C)0.2992
D)0.0487
E)0.3479
Q2) On a multiple choice test with 15 questions,each question has four possible answers,one of which is correct.For students who guess at all answers,find the standard deviation of the number of correct answers.
A)1.62
B)1.643
C)1.587
D)1.875
E)1.677
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Chapter 17: Sampling Distribution Models
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Sample Questions
Q1) A hair stylist believes the distribution of her tips is Normal,with a mean of $10.50 and a standard deviation of $6.25.What is the probability that her 15 clients this weekend will tip an average of less than $13?
A)0.0377
B)0.9394
C)0.4000
D)0.0606
E)0.6000
Q2) A candy company claims that its jelly bean mix contains 15% blue jelly beans.Suppose that the candies are packaged at random in small bags containing about 200 jelly beans.What is the probability that a bag will contain more than 12% blue jelly beans?
A)0.8625
B)0.117
C)0.234
D)0.9141
E)0.883
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Chapter 18: Confidence Intervals for Proportions
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Sample Questions
Q1) A laboratory tested 60 chicken eggs and found that the mean amount of cholesterol was 241 milligrams with s = 14.7 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
A)(230.2,237.8)
B)(231.5,248.6)
C)(231.7,250.3)
D)(233.4,248.6)
E)(231.7,250.5)
Q2) A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake.How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 6%?
A)188
B)461
C)376
D)267
E)Not enough information is given.
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20
Chapter 19: Testing Hypotheses About Proportions
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Sample Questions
Q1) A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program on a random sample size of 60 and found sick leave at 23%.Create a 95% confidence interval for the proportion of employee sick leave.
A)Based on the data,we are 95% confident the proportion of employee sick leave is between 14.9% and 37.1%.
B)Based on the data,we are 95% confident the proportion of employee sick leave is between 3.76% and 42.24%.
C)Based on the data,we are 95% confident the proportion of employee sick leave is between 14.9% and 34.1%.
D)Based on the data,we are 95% confident the proportion of employee sick leave is between 20% and 26%.
E)Based on the data,we are 95% confident the proportion of employee sick leave is between 12.4% and 33.6%.
Q2) A survey investigation whether the proportion of employees who commute by car to work is higher than it was five years ago finds a P-value of 0.009.Is it reasonable to conclude that more employees are commuting by car?
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21
Chapter 20: More About Tests
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Sample Questions
Q1) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,p,is less than 5%.Identify the Type II error in this context.
A)The error of rejecting the claim that the true proportion is less than 5% when it really is less than 5%.
B)The error of failing to reject the claim that the true proportion is at least 5% when it is actually less than 5%.
C)The error of accepting the claim that the true proportion is at least 5% when it really is at least 5%.
D)The error of rejecting the claim that the true proportion is at least 5% when it really is at least 5%.
E)The error of accepting the claim that the true proportion is at least 5% when it is actually less than 5%.
Q2) A dentist that is developing detection devices to search for tooth decay has concluded that his new device is significantly better than taking X-rays.He made this decision using = 0.05.Would he have made the same decision at = 0.10 and = 0.01?
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Chapter 21: Comparing Two Proportions
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Sample Questions
Q1) In a random sample of 300 Canadian women,68% watch CBC News.In a random sample of 200 Canadian men,56% watch CBC News.Construct a 98% confidence interval for the difference in the proportions of women and men who watch CBC News.
A)(0.017,0.234)
B)(0.033,0.207)
C)(0.017,0.223)
D)(0.029,0.211)
E)(0.006,0.234)
Q2) Suppose that you perform a two-proportion z-test and reject the null hypothesis that there is no difference in the two proportions.If that conclusion is actually wrong,which type of error did you commit?
Q3) You wish to construct a 90% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.03,what sample size should we take from each group? Assume equal sample sizes.
A)752
B)1504
C)1503
D)751
E)1984
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Page 23
Chapter 22: Inferences About Means
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Sample Questions
Q1) Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from 119.1 cm to 125.9 cm
A)1.7 cm
B)6.8 cm
C)3.4 cm
D)2.0 cm
E)Not enough information is given.
Q2) Analysis of a random sample of 250 Nova Scotia nurses produced a 95% confidence interval for the mean annual salary of $42,807 < (Nurse Salary)< $49,699.
A)About 95% of Nova Scotia nurses earn between $42,807 and $49,699.
B)We are 95% confident that the average nurse salary in the Canada is between $42,807 and $49,699.
C)About 95% of the nurses surveyed earn between $42,807 and $49,699.
D)We are 95% confident that the interval from $42,807 to $49,699 contains the true mean salary of all Nova Scotia nurses.
E)If we took many random samples of Nova Scotia nurses,about 95% of them would produce this confidence interval.
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Page 24
Chapter 23: Comparing Means
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Q1) You wish to construct a 95% confidence interval to compare the mean measurement for two groups.A small pilot study yields sample standard deviations of 10 and 15 for Group 1 and Group 2,respectively.If we wish to obtain a margin of error of at most 5,what sample size should we take from each group? Assume equal sample sizes.
A)46
B)50
C)48
D)47
E)49
Q2) Compare the technique for decision making about populations using the hypothesis test method and the confidence interval method.
Q3) When we fail to reject the null hypothesis,we
A)claim that a significant difference exists between groups.
B)have committed a Type I error.
C)have obtained a t-value greater than our critical t-value.
D)conclude that sampling variability is responsible for our obtained difference.
E)have committed a Type II error.
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25
Chapter 24: Paired Samples and Blocks
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Q1) Suppose x is a variable on each of two populations whose members can be paired and that a paired difference is the difference between the values of the variable x on the members of a pair.True or false? The mean of the paired differences equals the difference between the two population means.
A)False
B)True
Q2) A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music.He designs a dexterity test,and first gives it to his participants while classical music is playing,and then while no music is playing.
A)Paired t-test,since there are two sets of measurements on the same subjects,providing a natural linking.
B)1-sample t-test,since there is only one sample of subjects taking the dexterity tests.
C)Not enough information is given to determine the best type of test.
D)z-test,since the researcher can find the standard deviation of his population.
E)Two-sample t-test,since how a subject performs with music should have no influence on how he performs without music,creating two independent samples.
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26
Chapter 25: Comparing Counts
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Sample Questions
Q1) Test the claim that workplace accidents are distributed on workdays as follows: Monday 25%,Tuesday: 15%,Wednesday: 15%,Thursday: 15%,and Friday: 30%.
In a study of 100 workplace accidents,24 occurred on a Monday,15 occurred on a Tuesday,17 occurred on a Wednesday,18 occurred on a Thursday,and 26 occurred on a Friday.Use a 10% level of significance.
Q2) When performing a chi-square goodness-of-fit test,why do large values of the test statistic suggest that the variable does not have the distribution stated in the null hypothesis? Refer to the formula for the test statistic in your explanation.
Q3) Among the eastern provinces in 2010,states,Nova Scotia has 40% of the total population,New Brunswick has 33%,Newfoundland has 21%,and Prince Edward Island has 6%.A market researcher selects a sample of 1000 subjects in 2011,with 450 in Nova Scotia,340 in New Brunswich,150 in Newfoundland,and 60 in Prince Edward Island.Does the distribution of the sample agree with the population distribution? Use a 1% level of significance.
Q4) When performing a chi-square goodness-of-fit test,how are the expected frequencies obtained?
Q5) Explain why a chi-square goodness-of-fit test is always right-tailed.
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Chapter 26: Inferences for Regression
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Q1) In the context of regression analysis,the sum of the residuals is always zero.
A)True
B)False
Q2) If the assumptions for regression inferences are met,what would you expect to see when constructing a residual plot and a normal probability plot for the residuals?
Q3) When performing regression analysis,different samples will all yield the same sample regression line.
A)True
B)False
Q4) In the context of regression analysis,explain what is meant by the term "residual".
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Chapter 27: Analysis of Variance
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Q1) An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?
A)df-treatment = 4;df-error = 19
B)df-treatment = 3;df-error = 17
C)df-treatment = 3;df-error = 16
D)df-treatment = 4;df-error = 20
E)df-treatment = 3;df-error = 19
Q2) A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?
A)df-treatment = 4;df-error = 16
B)df-treatment = 3;df-error = 16
C)df-treatment = 4;df-error = 19
D)df-treatment = 3;df-error = 19
E)df-treatment = 3;df-error = 17
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29
Chapter 28: Multifactor Analysis of Variance
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Q1) A student runs an experiment to study the effect that a teacher has based on the size of their class.She uses 3 different teachers on 6 different class sizes.
A)Teacher SS: 3 df;Class size SS: 5 df;SSE: 10 df
B)Teacher SS: 2 df;Class size SS: 5 df;SSE: 11 df
C)Teacher SS: 2 df;Class size SS: 8 df;SSE: 11 df
D)Teacher SS: 2 df;Class size SS: 5 df;SSE: 10 df
E)Teacher SS: 3 df;Class size SS: 4 df;SSE: 12 df
Q2) A student runs an experiment to test how race car drivers and different tracks affect time.He uses 3 different drivers on 4 different tracks.He randomizes the trials,performing 4 runs under each treatment condition,carefully recording how many laps each driver completes on each different track.
Q3) A student runs an experiment to study the effect of gas brand and car type on mileage.She uses 3 different brands of gas on 4 different types of cars.
Q4) A student runs an experiment on test scores for males and females at different times of day.She uses 4 different times of day.
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Chapter 29: Multiple Regression
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Q1) Which measurement is the best predictor of calorie content,after allowing for the linear effects of the other variables in the model?
A)protein
B)sugar
C)carbohydrates
D)fat
E)fibre
Q2) Which measurement is the best predictor of salary,after allowing for the linear effects of the other variables in the model?
A)months of service
B)words per minute of typing speed
C)score on standardized test
D)years of education
E)ability to take dictation in words per minute
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Chapter 30: Multiple Regression Wisdom
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Q1) An actuary wishes to predict the life expectancy of a person based on several variables.One categorical variable of interest is their relationship statussingle,married,divorced,widowed,or common-law.If the actuary wished to include "relationship status" in a regression model,how many indicator variables would he/she need to use in the model?
A)4
B)2
C)3
D)5
E)1
Q2) What is the purpose of an indicator variable in a regression model?
A)An indicator variable allows us to increase our R-squared value.
B)An indicator variable allows us to include quantitative variables in our model.
C)An indicator variable allows us to fix violations of our constant variance assumption.
D)An indicator variable allows us to fix violations of our normality assumption.
E)An indicator variable allows us to include categorical variables in our model.
Q3) How would you interpret the coefficient of Science in the multiple regression?
Q4) How would you interpret the coefficient of sex in this model?
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Page 32
Chapter 31: Rank-Based Nonparametric Tests
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Q1) Fifty (50)students took a math test before and after tutoring.Of the 50 students,34 showed an improvement and 2 showed no change.After ranking the remaining 48 differences (before - after),it is found that T- = 873 and T+ = 303 Do the data suggest that the tutoring improves math scores? Conduct a Wilcoxon signed rank test using a 0.01 level of significance.
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Chapter 32: The Bootstrap
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Sample Questions
Q1) Consider the following sample of three measurements {4,8,13}.What is the probability of observing the distinct resample {8,8,8}?
A)1/3
B)0
C)1/27
D)1
E)1/8
Q2) Consider the following sample of three measurements {4,8,8}.How many distinct resamples are possible?
A)24
B)27
C)3
D)10
E)4
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