Introduction to Business Statistics
Mock Exam
Course Introduction
Introduction to Business Statistics provides students with a foundational understanding of statistical concepts and techniques essential for analyzing data in business contexts. Covering topics such as descriptive statistics, probability theory, sampling methods, hypothesis testing, regression analysis, and data interpretation, this course equips learners with the skills to make informed decisions based on quantitative information. Emphasis is placed on real-world applications, using statistical software to solve business problems and communicate findings effectively. By the end of the course, students will be able to apply statistical reasoning to support decision-making processes in various business environments.
Recommended Textbook
Statistics for Business and Economics 8th Edition by Betty Newbold
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Page 2
Chapter 1: Describing Data: Graphical
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Sample Questions
Q1) The nominal level of measurement indicates the rank ordering of items.
A)True
B)False
Answer: False
Q2) Shoe size is an example of interval scale.
A)True
B)False
Answer: True
Q3) Making the heights of the bars but not the areas in a histogram proportional to the frequencies provides for a(n):
A)balanced histogram
B)misleading histogram
C)symmetrical histogram
D)accurate histogram
Answer: B
Q4) What is the total defect count in the report?
Answer: 180 defects
Q5) Give an example of a question where testing a hypothesis about a parameter would be helpful.
Answer: Are weekend sales at least 25% higher than weekday sales?
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Chapter 2: Describing Data: Numerical
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Sample Questions
Q1) If the mean of a symmetrical data set is less than the median,the data are considered to be negatively skewed.
A)True
B)False
Answer: True
Q2) The advantage of Chebyshev's theorem is that its applicability extends to any population regardless of its shape.However,it is within this guarantee that its major drawback lies.
A)True
B)False Answer: True
Q3) The five-number summary refers to the five descriptive measures: minimum,mean,median,mode,and maximum;therefore it is sometimes known as the five-m summary.
A)True
B)False Answer: False
Q4) Calculate the correlation coefficient between the size of the sales force and gross sales.
Answer: r = 0.765
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Chapter 3: Probability
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Sample
Questions
Q1) Which of the following statements is true for any two events A and B defined on a sample space S?
A)If the intersection of events A and B is the empty set,then A and B are collectively exhaustive.
B)If the union of events A and B is the empty set,then each of A and B is the empty set.
C)If events A and B are collectively exhaustive,then A B .
D)If events A and B are mutually exclusive and collectively exhaustive,then the union of A and B is not necessarily the sample space.
Answer: B
Q2) If two events are mutually exclusive,they must also be collectively exhaustive. A)True
B)False
Answer: False
Q3) If an event and its complement are equally likely to occur,the probability of that event must be 0.50.
A)True
B)False
Answer: True
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5
Chapter 4: Discrete Random Variables and Probability
Distributions
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Sample Questions
Q1) A perfect straight line sloping downward would produce a covariance value of -1.
A)True
B)False
Q2) What is P(X < 6)?
Q3) What is the standard deviation of the weight of cereal in the boxes?
A)0.81
B)1.25
C)0.90
D)1.19
Q4) What is the value of Var(2X - 3Y)?
A)-0.2425
B)3.2275
C)3.0775
D)3.5275
Q5) The number of accidents on a US -131 highway average 4.4 per year.Assuming that the number of accidents follows a Poisson distribution,what is the probability that there are more than three accidents next year on US - 131?
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Q6) What is the probability that exactly 18 customers purchase running shoes?
Q7) Identify the variance of weekly take-home pay.
Q8) Find the probability distribution of the random variable X + Y.
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Page 7
Chapter 5: Continuous Random Variables and Probability
Distributions
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Sample Questions
Q1) The mean and variance of any normal distribution are always zero and one,respectively.
A)True
B)False
Q2) When we convert normal distributions to the standard normal distribution,we are essentially making them all alike.How is this possible and what are the implications?
Q3) The normal distribution is useful for waiting-line or queuing problems and service-time problems.
A)True
B)False
Q4) The distribution that has been found to be particularly useful for waiting-line or queuing problems is referred to as the:
A)exponential distribution.
B)hypergeometric distribution.
C)marginal distribution.
D)standard normal distribution.
Q5) With probability 0.20,the number of successes is greater than how many?
Q6) Find the probability that X is greater than 58.
Q7) Find the probability that the number of successes is greater than 775.
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Chapter 6: Sampling and Sampling Distributions
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Sample Questions
Q1) What is the probability that the sample proportion is greater than 0.60?
Q2) A sample of size 25 is selected at random from a finite population.If the finite population correction factor is 0.80,then the population size is:
A)121
B)96
C)75
D)100
Q3) The average score of all students who took a particular statistics class last semester has a mean of 70 and a standard deviation of 3.0.Suppose 36 students who are taking the class this semester are selected at random.Find the probability that the average score of the 36 students exceeds 71.
A)0.0228
B)0.0772
C)0.1228
D)0.1772.
Q4) What is the mean of the sampling distribution of the sample proportion of returns leading to refunds?
Q5) What are the mean and standard error of the sampling distribution for the mean score?
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Chapter 7: Estimation: Single Population
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Sample Questions
Q1) The probability density functions of normal distributions and t distributions are symmetric about their means.
A)True
B)False
Q2) What is the relative efficiency of Z with respect to Y?
A)0.50
B)0.80
C)1.20
D)1.50
Q3) Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $95,000.
Q4) If a sample of size 21 is selected,the value of A for the probability P(t A)= 0.025 is:
A)2.528
B)2.086
C)2.518
D)2.080
Q5) Give a careful verbal interpretation of the 99% confidence interval for the population mean.
Q6) Check for evidence of nonnormality.
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Chapter 8: Estimation: Additional Topics
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Sample Questions
Q1) Find the margin of error for a 95% confidence interval for the difference in the means of the two populations assuming that the population variances are equal.
A)4.002
B)4.767
C)5.365
D)3.645
Q2) The Student's t-distribution is required to determine the confidence interval for the difference between two normal population means with unknown population variances.
A)True
B)False
Q3) What is the upper confidence limit of the 95% confidence interval?
A)16.879
B)12.987
C)15.233
D)14.767
Q4) Find the upper confidence limit of the 99% confidence interval for the difference between the means of the two populations.
Q5) Calculate the width of the interval for a 95% confidence interval.
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Chapter 9: Hypothesis Testing: Single Population
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Sample Questions
Q1) What are the appropriate null and alternative hypotheses?
Q2) Which of the following statements is most accurate?
A)reject the null hypothesis at = 0.10
B)fail to reject the null hypothesis at 0.10
C)reject the null hypothesis at = 0.05,but not 0.10
D)reject the null hypothesis at = 0.01,but not 0.05
Q3) When testing H<sub>0</sub> : = 50 against H<sub>1</sub> : 50,where would the rejection region fall for this hypothesis test?
A)in the left tail
B)in the right tail
C)in both the left and right tails
D)at point zero
Q4) The larger the sample size,the greater the power of the test with everything else being equal.
A)True
B)False
Q5) Explain the distinction between Type I and Type II errors.
Q6) Calculate the sample mean and sample standard deviation.
Q7) State the appropriate null and alternative hypotheses.
Q8) Calculate the sample variance.
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Chapter 10: Hypothesis Testing: Additional Topics
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Sample Questions
Q1) Based on the given information,the p-value for the F test of equal variances can be calculated and shown to be 0.289.Based on this p-value,what is your conclusion?
A)The assumption of equal variances is correct.
B)The assumption of equal variances is incorrect.
C)The answer cannot be determined based on this p-value.
D)The variance of the first sample is greater than the other.
Q2) In order to test if the diet is effective,what is the appropriate alternative hypothesis?
A)H<sub>1</sub> : <sub>d</sub> < 0
B)H<sub>1</sub> : <sub>d</sub> > 0
C)H<sub>1</sub> : <sub>d</sub> = 0
D)H<sub>1</sub> : <sub>d</sub> 0
Q3) In testing for differences between the means of two independent populations if the test statistic is very large,then the p-value of the test should be very small.
A)True
B)False
Q4) State the null and alternative hypotheses.
Q5) Use Excel or Minitab to summarize the data using descriptive statistics.
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Chapter 11: Simple Regression
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Sample Questions
Q1) The t-test for the true slope <sub>1</sub> = 0 is identical to the t-test for the true correlation = 0.
A)True
B)False
Q2) The residual and the model error are equivalent concepts.
A)True
B)False
Q3) The value of the coefficient of determination can never be larger than 1.0.
A)True
B)False
Q4) The regression sum of squares represents the variability that is explained by the intercept of the regression equation.
A)True
B)False
Q5) The coefficient of determination is the positive square root of the coefficient of correlation.
A)True
B)False
Q6) Determine the coefficient of correlation.What does it mean?
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Chapter 12: Multiple Regression
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Sample Questions
Q1) What should the null and alternative hypotheses be for <sub>2</sub>?
A)H<sub>0</sub> : <sub>2</sub><sub> </sub>= 0,<sub> </sub>H<sub>1</sub> :<sub> </sub> <sub>2</sub> > 0
B)H<sub>0</sub> : <sub>2</sub><sub> </sub> 0,<sub> </sub>H<sub>1</sub><sub> </sub>:<sub> </sub> <sub>2</sub> = 0
C)H<sub>0</sub> : <sub>2</sub> > 0,<sub> </sub>H<sub>1</sub><sub> </sub>:<sub> </sub> <sub>2</sub><sub> </sub>< 0
D)H<sub>0</sub> : <sub>2</sub> = 0,<sub> </sub>H<sub>1</sub><sub> </sub>: <sub>2</sub><sub> </sub> 0
Q2) Find a 95% confidence intervals for <sub>3</sub>.
Q3) Is there enough evidence at the 10% significance level to infer that the model is useful in predicting how long an individual will live?
Q4) Compute the coefficient b<sub>2</sub>.
Q5) The coefficient of multiple correlation R measures the strength of the relationship between the dependent variable and the independent variables.
A)True
B)False
Q6) Compute the adjusted coefficient of determination.
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Chapter 13: Additional Topics in Regression Analysis
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Sample Questions
Q1) The model y<sub>t</sub> = 8 + 2.1x<sub>t</sub><sub> </sub>+ 0.25y<sub>t</sub><sub>-1</sub> is estimated using regression analysis applied to time-series data.What is the effect of a 1-unit increase in x in period (t + 1)?
Q2) Test the hypotheses H<sub>0</sub> : There is no first-order autocorrelation vs.H<sub>1</sub>: There is positive first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.12,n = 45,k = 5,and = 0.05
Q3) Briefly discuss approaches that can be employed in situations where multicollinearity is detected.
Q4) If X<sub>1</sub> were to increase by 1-unit in time t,by how much would we expect Y to change over all current and future time periods as a result of this increase?
A)45.13
B)28.85
C)17.99
D)34.59
Q5) Describe a formal test for heteroscedasticity.Explain why a test with this design is likely to identify heteroscedasticity.
Q6) Test the model for heteroscedasticity.
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Page 16
Chapter 14: Analysis of Categorical Data
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Sample Questions
Q1) If the number n of non-zero sample observations is large,then the sign test is based on the normal approximation to the binomial with mean = 0.5n and variance <sup>2</sup> = 0.25n.
A)True
B)False
Q2) The Wilcoxon signed rank test statistic is approximately normally distributed whenever the number n of nonzero differences in the sample is larger than: A)10
B)20
C)5
D)15
Q3) A nonparametric method that is equivalent to the Wilcoxon rank sum test is the: A)Wilcoxon signed rank test.
B)Sign test.
C)Spearman rank correlation test.
D)Mann-Whitney U test.
Q4) Is there sufficient evidence to reject the null hypothesis of no preference against a two-sided alternative?
Q5) Which test is used for testing the hypotheses above?
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Chapter 15: Analysis of Variance
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Sample Questions
Q1) Develop the analysis of variance table.
Q2) In a two-way ANOVA,the interpretations of the group effects make sense only when the interaction component is not significant.
A)True
B)False
Q3) What is the total for the sum of squares?
A)2476.33
B)960.7
C)3437.02
D)4397.72
Q4) Is there sufficient evidence to reject the null hypothesis that the average number of machines per order is the same for different regions of the country?
Q5) Set up the two-way ANOVA table.
Q6) Subject to the value of the sample sizes,the MSE can be negative or positive. A)True
B)False
Q7) Test the null hypothesis of no interaction between student year and dormitory rating.
Q8) Complete the ANOVA table.
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Chapter 16: Time-Series Analysis and Forecasting
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Sample Questions
Q1) Calculate the forecast value for the year 1905,if the real home price index for that year is 98.056.
A)100.31
B)98.51
C)98.06
D)cannot be determined
Q2) Compute the sales forecast for the 1<sup>st</sup> quarter of year 4.
A)approximately 113 units
B)approximately 269 units
C)approximately 164 units
D)approximately 369 units
Q3) The number of four-period centered moving averages of a time series with 20 time periods is:
A)28
B)24
C)20
D)16
Q4) Develop a centered 4- point moving average for this time series.
Q5) Use a smoothing constant of 0.8 to show the table that shows all the forecast values for the given series.
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Chapter 17: Additional Topics in Sampling
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Sample Questions
Q1) If a total sample of 120 students is taken,determine the number of juniors and seniors under the proportional allocation scheme.
Q2) Find a 95% confidence interval for the total amount of the 800 accounts receivable.
Q3) Find a 95% confidence interval for the total dollar value of these invoices.
A)60,1704 ± 10258.15
B)60,1704 ± 8168.36
C)60,1704 ± 15987.64
D)60,1704 ± 22481.79
Q4) A sales representative has 850 accounts.She is interested in determining the proportion of her accounts that have placed an order within the past month.For a standard deviation of 0.5,how large a sample should she take in order to estimate the population proportion within five percent at a 95% level of confidence?
Q5) For a sample of 126 observations from a population of 873,the sample mean is 17.2 and the sample standard deviation is 2.4.Create a 99% confidence interval for the population mean.
Q6) Explain in detail what is meant by "cluster sampling has a superficial resemblance to stratified sampling."
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