Decision Making with Statistics
Final Test Solutions
Course Introduction
This course explores the use of statistical methods to support effective decision making in business, policy, and everyday contexts. Students will learn to apply principles of probability, descriptive and inferential statistics, hypothesis testing, and regression analysis to interpret data and make informed choices. Emphasis is placed on understanding data-driven reasoning, interpreting results critically, and communicating statistical findings clearly. Through real-world case studies and hands-on exercises, learners develop practical skills to analyze uncertainty, assess risks, and optimize outcomes in various decision-making scenarios.
Recommended Textbook
Statistics for Business and Economics 8th Edition by Betty Newbold
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17 Chapters
3406 Verified Questions
3406 Flashcards
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Page 2
Chapter 1: Describing Data: Graphical
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247 Verified Questions
247 Flashcards
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Sample Questions
Q1) Which of the following statements about a pie chart is false?
A)A pie chart is graphical representation of the proportion or percentage of frequency of each category of a categorical variable.
B)A pie chart is usually used to display the relative sizes of categories of a numerical variable.
C)A pie chart always has the shape of a circle.
D)The size of each slice of a pie chart is the proportion or percentage of frequency of the corresponding category of a categorical variable.
Answer: B
Q2) Describe the population.
Answer: All boxes of pencils in the warehouse
Q3) Descriptive statistics transform data into information.
A)True
B)False
Answer: True
Q4) A histogram is the best graphical tool to display qualitative data. A)True
B)False
Answer: False
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Chapter 2: Describing Data: Numerical
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326 Flashcards
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Sample Questions
Q1) Suppose you are told that the mean of a sample is below the median.What does this information suggest about the distribution?
A)The distribution is symmetric.
B)The distribution is skewed to the right or positively skewed.
C)The distribution is skewed to the left or negatively skewed.
D)There is insufficient information to determine the shape of the distribution.
Answer: C
Q2) Which of the following statements is not true?
A)The 75<sup>th</sup> percentile is equal to 23.5.
B)The median is equal to the mode.
C)The mean is 19.9.
D)The distribution is approximately symmetric.
Answer: A
Q3) The standard deviation of the number of miles driven by the ten employees is: Answer: 5.28
Q4) Positive skewness results if a distribution is skewed to the left.
A)True
B)False
Answer: False
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Chapter 3: Probability
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Sample Questions
Q1) The probability of not an increase in interest rates and not a decrease in house sales is:
A)0.50
B)0.35
C)0.20
D)0.05
Answer: B
Q2) The sum of the probabilities of collectively exhaustive events must equal 1.
A)True
B)False
Answer: False
Q3) If P(A)= 0.84,P(B)= 0.76,and P(A ,and P(A B) = 0.90, then P(A B) is:
A) 0.06
B) 0.14
C) 0.70
D) 0.83
Answer: C
Q4) Calculate the probability that a plane leaves on time.
Answer: P(D)= P(A D)+ P(B D)+ P(C D)= 0.48 + 0.18 + 0.049 = 0.709
5
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Chapter 4: Discrete Random Variables and Probability
Distributions
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Sample Questions
Q1) Identify the variance of amount spent weekly on recreational activities.
Q2) Thirty percent of all households have a DVD player.If you select 20 houses at random,what is the probability that six or fewer of them have a DVD player?
A)0.608
B)0.416
C)0.344
D)0.238
Q3) Identify the variance of weekly take-home pay.
Q4) Are X and Y statistically independent? Explain.
Q5) Find the probability the next inspected disk will have no missing pulse.
Q6) The Bernoulli model yields just two possible mutually exclusive and collectively exhaustive outcomes,which are labeled success and failure.
A)True
B)False
Q7) What is the probability that at least 17 customers purchase running shoes?
Q8) Using the Poisson approximation to the binomial,how likely is it to get exactly four defects out of 100?
Q9) Compute the covariance between X and Y. Page 6
Q10) What is the probability that no more than 19 customers purchase running shoes?
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Chapter 5: Continuous Random Variables and Probability
Distributions
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239 Flashcards
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Sample Questions
Q1) The profit for a production process is equal to $7,200 minus 2.8 times the number of units produced.The mean and variance for the number of units produced are 1,100 and 800,respectively.Find the mean and variance of the profit.
Q2) What proportion of the total area under the normal curve is above the mean?
A)50%
B)68%
C)95%
D)99.7%
Q3) Given the random variables X and Y have a correlation coefficient equal to 0.50,find the mean and variance of the random variable W = 4X - 3Y.
Q4) The total area under the curve of the probability density function of any normal distribution is always 1.0.
A)True
B)False
Q5) Find the value k such that P(Z > k)= 0.83
Q6) Find the value k such that P(0 < Z < k)= 0.35
Q7) Find the probability that the percentage of successes is greater than 0.42
Q8) Find the 95<sup>th</sup> percentile.
Page 8
Q9) What is the probability that x is between 1 and 3?
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Page 9
Chapter 6: Sampling and Sampling Distributions
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Sample Questions
Q1) What is the probability that for a sample of 30 bottles,the sample variance is greater than 0.5?
Q2) The central limit theorem is basic to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data.
A)True
B)False
Q3) What is the name of the parameter that determines the shape of the chi-square distribution?
A)mean
B)variance
C)proportion
D)degrees of freedom
Q4) Acceptance intervals are widely used for quality control monitoring of various production and service processes.
A)True
B)False
Q5) The probability is 0.025 that the sample standard deviation is smaller than what value?
Q6) Find the population mean and population standard deviation.
Page 10
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Chapter 7: Estimation: Single Population
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Sample Questions
Q1) The sample standard deviation s is an unbiased estimator of the population standard deviation .
A)True
B)False
Q2) Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?
A)the t distribution with n + 1 degrees of freedom
B)the t distribution with n degrees of freedom
C)the t distribution with n - 1 degrees of freedom
D)the t distribution with 2n degrees of freedom
Q3) Calculate a 95% confidence interval for the population mean.
Q4) In a survey of 472 personnel directors,63% thought that they would be hiring new personnel over the next three months.Which of the following represents a 98% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?
A)0.63 ± 0.057
B)0.63 ± 0.047
C)0.63 ± 0.042
D)0.63 ± 0.052
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Chapter 8: Estimation: Additional Topics
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Sample Questions
Q1) Find the width of the 99% confidence interval.
Q2) A 95% confidence interval estimate for the difference between two population means, <sub>1</sub> - <sub>2</sub>,is determined to be 62.75 < <sub>1</sub><sub>2</sub> < 68.52.Which of the following is true if the confidence level is reduced to 90%?
A)The confidence interval becomes wider.
B)The confidence interval remains the same.
C)The confidence interval becomes narrower.
D)More information is required to determine the answer.
Q3) Calculate the margin of error.
A)3.32
B)2.26
C)2.05
D)1.82
Q4) Find the lower confidence limit of the 99% confidence interval for the difference between the means of the two populations.
Q5) Find a 90% confidence interval for the difference in average functioning time before recharging the two models.
Q6) Calculate the width of the interval for a 90% confidence interval.
Page 12
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Chapter 9: Hypothesis Testing: Single Population
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Sample Questions
Q1) Provide the test for mean of a normal distribution with population variance unknown,with the null hypothesis H<sub>0</sub> : <sub>0</sub>
Q2) A company produces electrical devices operated by a thermostatic control.According to the engineering specifications,the standard deviation of the temperature at which these controls actually operate should not exceed 2.0 degrees Fahrenheit.For a random sample of 25 of these controls,the sample standard deviation of operating temperatures was 2.36 degrees Fahrenheit.Stating any assumptions you need to make,test at the 5% level the null hypothesis that the population standard deviation is at most 2.0 against the alternative that is bigger.
Q3) Match the symbol with the correct definition.
A)the power of a test
B)the probability of a Type I error
C)the probability of a Type II error
D)the probability of failing to reject the null hypothesis when it is true
Q4) Explain carefully the distinction between simple and composite hypotheses.
Q5) Calculate the sample variance.
Q6) Compute the probability of Type II error and the power of the test for = 4.04.
Q7) Test the hypothesis at the 5% level.
Q8) In this test,what would be a Type I error?
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Chapter 10: Hypothesis Testing: Additional Topics
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103 Flashcards
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Sample Questions
Q1) The F test used for testing the difference in two population variances is always a one-tailed test.
A)True
B)False
Q2) A random sample of 1500 people from the town of Sotown were asked if they thought that the Boston Red Sox would win the next World Series.78% of the sample thought that the Boston Red Sox would win.But when a random sample of 1500 people from the town of Michika was asked the same question,65% thought that the Boston Red Sox would win the next World Series.Does this provide strong evidence at the 5% significance level that the people in Sotown are more optimistic about the Boston Red Sox's chances of winning the next World Series?
Q3) Using results of Excel or Minitab to conduct a two-sample t-test,test
H<sub>0</sub> : <sub>1</sub> - <sub>2</sub> 0 vs.H<sub>1</sub> : <sub>1</sub><sub>2</sub> > 0 at the 5% significance level.
Q4) In practical applications,the F ratio is arranged in a way such that the larger sample variance is in the denominator and the smaller is in the numerator.
A)True
B)False
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Page 14
Chapter 11: Simple Regression
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Sample Questions
Q1) Calculate the slope coefficient.
Q2) In a study it was shown that for a sample of 375 college faculty the correlation was 0.15 between annual raises and teaching evaluations.What would be the coefficient of determination of a regression of annual raises on teaching evaluations for this sample? Interpret your results.
Q3) Which value of the following values of coefficients of correlation indicates a stronger correlation than 0.50?
A)-0.40
B)-0.60
C)+0.40
D)+0.53
Q4) Test the hypotheses H<sub>0</sub> : <sub>1</sub> = 0 vs.H<sub>1</sub> : <sub>1</sub> 0 using the F statistic.
Q5) What is the y-intercept of the regression line of hours on income?
A)64.23
B)36.43
C)46.23
D)23.46
Q6) Compute the error sum of squares,SSE.
Page 15
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Chapter 12: Multiple Regression
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Sample Questions
Q1) Determine the coefficient of multiple correlation.
A)0.42
B)0.82
C)0.73
D)0.91
Q2) By transforming the variables,we can estimate a linear multiple regression model and use the results as a nonlinear model.
A)True
B)False
Q3) Calculate the error sum of squares.
Q4) What would you expect regarding these population regression parameters?
Q5) For a fixed weekly income,test the null hypothesis that milk consumption does not depend linearly on the size of the family against an appropriate one-sided alternative.Use = 0.025.
Q6) The multiple coefficient of determination R<sup>2</sup> can only be used to compare regression models that have the same set of sample observations of y<sub>i</sub>,where i =1,2, ,n.
A)True
B)False
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Chapter 13: Additional Topics in Regression Analysis
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Sample Questions
Q1) Do these results allow us,at the 5% significance level,to conclude that the model is useful in predicting the price of gold?
Q2) When the errors in a regression model are correlated,the coefficient estimates are biased and efficient.
A)True
B)False
Q3) Determine if there is sufficient evidence at the 5% significance level to infer that the relationship between x and y is significant.
Q4) 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)?
Q5) Explain what is meant by multicollinearity.What effects does multicollinearity have on the results of regression coefficients?
Q6) If omitted variables are uncorrelated with the other independent variables,a bias in the estimation of coefficients occurs.
A)True B)False
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Page 17
Chapter 14: Analysis of Categorical Data
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Sample Questions
Q1) In all the rank tests,normality is a required assumption for the underlying populations.
A)True
B)False
Q2) When testing for independence in a contingency table with r rows and c columns,the degrees of freedom for the test statistic would be:
A)r + c + 1
B)r + c -1
C)(r-1)(c-1)
D)rc - 1
Q3) Which nonparametric method is appropriate for analyzing these results?
Q4) Which of the following should certainly be known to select a value in the chi-square distribution table?
A)the mean and the variance of the observations
B)the level of significance and the variance of the observations
C)the degrees of freedom and the mean of the observations
D)the level of significance and the degrees of freedom
Q5) Is there sufficient evidence of student support for the new mascot?
Q6) Test whether the students did better on the second exam than the first.
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Chapter 15: Analysis of Variance
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Sample Questions
Q1) Compute mean squares for between groups.
Q2) State the decision rule for the Kruskal-Wallis test at the 0.05 level of significance.
Q3) What is the value of "G"?
A)1.350
B)1.192
C)1.421
D)1.820
Q4) Perform a two-way ANOVA with this data.
Q5) Is there sufficient evidence to reject H<sub>0</sub> that the average between different regions is the same?
A)Reject H<sub>0</sub><sub> </sub>for = 0.01.
B)Reject H<sub>0</sub> for = 0.005.
C)Reject H<sub>0</sub><sub> </sub>for = 0.05.
D)Unable to reject H<sub>0</sub><sub> </sub>for < 0.10.
Q6) What is the mean square value for Error?
A)429.63
B)121.85
C)394.06
D)129.42
Page 19
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Chapter 16: Time-Series Analysis and Forecasting
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Sample Questions
Q1) Which of the following has an approximate forecast of 270 units?
A)year 1 quarter 4
B)year 6 quarter 3
C)year 5 quarter 4
D)year 4 quarter 3
Q2) Seasonality is a time-series component.
A)True
B)False
Q3) How do you remove the seasonality component from the given time series.
Q4) Which of the following weeks has a level estimate of 672 units approximately?
A)week 5
B)week 7
C)week 9
D)week 13
Q5) What is the seasonal index for quarter 2?
A)141.99
B)84.53
C)83.13
D)91.52
Q6) Assuming a smoothing constant of 0.8,find the error term for the year 1936.
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Chapter 17: Additional Topics in Sampling
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Sample Questions
Q1) Find a 95% confidence interval for the mean monthly expenditures.
Q2) Find a 98% confidence interval for the total expenditures.
A)13,128.01 ± 126.71
B)13,128.01 ± 581.23
C)13,128.01 ± 342.58
D)13,128.01 ± 665.49
Q3) Find a 90% confidence interval for the mean rating given by all juniors and seniors on the campus.
A)4.65 ± 0.369
B)4.65 ± 0.183
C)4.65 ± 0.254
D)4.65 ± 0.513
Q4) Using an unbiased estimation procedure,find an estimate of the variance of the sample mean.
Q5) The distinction between cluster sampling and stratified sampling is that in the former a random sample of clusters is taken,while in the latter a complete census of stratum members is drawn.
A)True
B)False
Q6) Estimate the proportion of all students going on the field trip.
Page 21
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