Statistics for Business Analytics

1. What is the main purpose of descriptive statistics?

a) To make inferences about a population
b) To describe the main features of a dataset
c) To determine cause and effect
d) To test hypotheses
Answer: b) To describe the main features of a dataset

2. Which measure of central tendency is most affected by extreme values?

a) Mean
b) Median
c) Mode
d) Range
Answer: a) Mean

3. Which of the following is a measure of variability?

a) Mean
b) Median
c) Standard deviation
d) Mode
Answer: c) Standard deviation

4. What does a p-value signify in hypothesis testing?

a) The probability that the null hypothesis is true
b) The probability of observing the data given that the null hypothesis is true
c) The probability of a Type II error
d) The probability of rejecting the null hypothesis when it is true
Answer: b) The probability of observing the data given that the null hypothesis is true

5. Which type of chart is best for displaying the relationship between two variables?

a) Histogram
b) Bar chart
c) Pie chart
d) Scatter plot
Answer: d) Scatter plot

6. In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

a) 50%
b) 68%
c) 95%
d) 99.7%
Answer: b) 68%

7. Which of the following best describes the term “outlier”?

a) The most frequently occurring value
b) A data point that is significantly different from other data points
c) The midpoint of a dataset
d) A value that represents the central location of a dataset
Answer: b) A data point that is significantly different from other data points

8. What is the purpose of regression analysis in business analytics?

a) To summarize data
b) To predict the value of a dependent variable based on an independent variable
c) To determine the mode of a dataset
d) To compare the means of two groups
Answer: b) To predict the value of a dependent variable based on an independent variable

9. What is a Type I error in hypothesis testing?

a) Failing to reject a true null hypothesis
b) Rejecting a true null hypothesis
c) Failing to reject a false null hypothesis
d) Rejecting a false null hypothesis
Answer: b) Rejecting a true null hypothesis

10. What does R-squared measure in regression analysis?

a) The correlation between two variables
b) The proportion of variance in the dependent variable explained by the independent variable
c) The difference between observed and predicted values
d) The significance level of the regression coefficients
Answer: b) The proportion of variance in the dependent variable explained by the independent variable

11. What is the primary use of the Central Limit Theorem?

a) To describe the variability of a dataset
b) To understand the distribution of sample means
c) To calculate probabilities for a normal distribution
d) To test hypotheses about population parameters
Answer: b) To understand the distribution of sample means

12. What is multicollinearity in multiple regression analysis?

a) When independent variables are highly correlated with each other
b) When the dependent variable is highly correlated with the independent variables
c) When there are too many independent variables
d) When the regression model does not fit the data well
Answer: a) When independent variables are highly correlated with each other

13. Which statistical test is used to compare the means of three or more groups?

a) t-test
b) Chi-square test
c) ANOVA (Analysis of Variance)
d) Regression analysis
Answer: c) ANOVA (Analysis of Variance)

14. What is the main advantage of using a box plot?

a) It shows the frequency distribution of data
b) It displays the relationship between two variables
c) It provides a summary of the minimum, first quartile, median, third quartile, and maximum
d) It shows the mode of the dataset
Answer: c) It provides a summary of the minimum, first quartile, median, third quartile, and maximum

15. What does a correlation coefficient of -1 indicate?

a) No correlation
b) A perfect positive correlation
c) A perfect negative correlation
d) A moderate negative correlation
Answer: c) A perfect negative correlation

16. Which measure of central tendency can be used for categorical data?

a) Mean
b) Median
c) Mode
d) Standard deviation
Answer: c) Mode

17. What is the purpose of a confidence interval?

a) To estimate the range in which a population parameter lies with a certain level of confidence
b) To determine the mode of a dataset
c) To test the significance of a hypothesis
d) To calculate the mean of a dataset
Answer: a) To estimate the range in which a population parameter lies with a certain level of confidence

18. What is heteroscedasticity in regression analysis?

a) When the residuals are normally distributed
b) When the residuals have constant variance
c) When the residuals have non-constant variance
d) When the regression model has high explanatory power
Answer: c) When the residuals have non-constant variance

19. Which of the following is an example of a non-parametric test?

a) t-test
b) ANOVA
c) Chi-square test
d) Regression analysis
Answer: c) Chi-square test

20. What does the term “sampling error” refer to?

a) Errors that occur during data collection
b) The difference between a sample statistic and the corresponding population parameter
c) Mistakes made during data entry
d) Errors due to non-response in a survey
Answer: b) The difference between a sample statistic and the corresponding population parameter

21. Which of the following is used to measure the strength and direction of a linear relationship between two variables?

a) Mean
b) Standard deviation
c) Correlation coefficient
d) Variance
Answer: c) Correlation coefficient

22. What is the purpose of a Pareto chart in business analytics?

a) To show the distribution of a dataset
b) To identify the most significant factors in a dataset
c) To display the relationship between two variables
d) To compare the means of two groups
Answer: b) To identify the most significant factors in a dataset

23. Which of the following best describes a time series analysis?

a) Analysis of data at a single point in time
b) Analysis of data over a period of time
c) Comparison of means between two groups
d) Analysis of categorical data
Answer: b) Analysis of data over a period of time

24. What is the null hypothesis in a hypothesis test?

a) A statement that there is an effect or difference
b) A statement that there is no effect or difference
c) A statement about the sample mean
d) A statement about the population variance
Answer: b) A statement that there is no effect or difference

25. What is the main purpose of inferential statistics?

a) To summarize data
b) To make conclusions about a population based on a sample
c) To describe the main features of a dataset
d) To test hypotheses
Answer: b) To make conclusions about a population based on a sample

26. What does a scatter plot best represent?

a) The frequency distribution of data
b) The relationship between two continuous variables
c) The central tendency of data
d) The variability of data
Answer: b) The relationship between two continuous variables

27. In hypothesis testing, what is the power of a test?

a) The probability of rejecting the null hypothesis when it is false
b) The probability of accepting the null hypothesis when it is true
c) The probability of observing the data given that the null hypothesis is true
d) The significance level of the test
Answer: a) The probability of rejecting the null hypothesis when it is false

28. Which measure of central tendency is appropriate for nominal data?

a) Mean
b) Median
c) Mode
d) Range
Answer: c) Mode

29. What is the main advantage of using a stem-and-leaf plot?

a) It provides a visual summary of the data
b) It shows the relationship between two variables
c) It displays the frequency of data
d) It retains the original data values
Answer: d) It retains the original data values

30. In regression analysis, what does the term “residual” refer to?

a) The predicted value of the dependent variable
b) The difference between the observed and predicted values
c) The slope of the regression line
d) The intercept of the regression line
Answer: b) The difference between the observed and predicted values

31. What is the purpose of the Durbin-Watson statistic?

a) To test for normality
b) To test for autocorrelation
c) To test for heteroscedasticity
d) To test for multicollinearity
Answer: b) To test for autocorrelation

32. Which of the following is a graphical representation of the five-number summary?

a) Histogram
b) Box plot
c) Scatter plot
d) Pareto chart
Answer: b) Box plot

33. What is the main goal of clustering in data analysis?

a) To find patterns or groupings in the data
b) To predict the value of a dependent variable
c) To test the significance of differences between groups
d) To measure the strength of relationships between variables
Answer: a) To find patterns or groupings in the data

34. What is a major assumption of parametric tests?

a) Data must be normally distributed
b) Data must be categorical
c) Data must be ordinal
d) Data must be non-normally distributed
Answer: a) Data must be normally distributed

35. What does the term “bivariate analysis” refer to?

a) Analysis of one variable
b) Analysis of two variables
c) Analysis of three variables
d) Analysis of more than three variables
Answer: b) Analysis of two variables

36. In a chi-square test, what is the null hypothesis usually stating?

a) There is a significant relationship between variables
b) The variables are independent
c) The means of two groups are equal
d) The data follows a normal distribution
Answer: b) The variables are independent

37. Which test is appropriate for comparing the means of two independent groups?

a) ANOVA
b) t-test
c) Chi-square test
d) Regression analysis
Answer: b) t-test

38. What is the main focus of survival analysis?

a) To analyze the time until an event occurs
b) To compare the means of different groups
c) To test the significance of relationships between variables
d) To describe the distribution of a dataset
Answer: a) To analyze the time until an event occurs

39. What is the significance of the F-test in ANOVA?

a) To test the equality of variances
b) To test the significance of regression coefficients
c) To compare the means of two groups
d) To determine the goodness-of-fit of a model
Answer: a) To test the equality of variances

40. Which of the following is NOT a common assumption of linear regression?

a) Linearity
b) Homoscedasticity
c) Independence
d) Normality of residuals
Answer: c) Independence

41. What is the purpose of a control chart in quality control?

a) To display the distribution of data
b) To monitor the stability of a process over time
c) To identify relationships between variables
d) To test hypotheses about means
Answer: b) To monitor the stability of a process over time

42. What does the term “effect size” refer to in hypothesis testing?

a) The size of the sample used in the study
b) The magnitude of the difference or relationship being tested
c) The probability of making a Type I error
d) The significance level of the test
Answer: b) The magnitude of the difference or relationship being tested

43. Which test is used to determine if there is a significant difference between the variances of two populations?

a) t-test
b) Chi-square test
c) F-test
d) ANOVA
Answer: c) F-test

44. What does the term “bias” refer to in statistical analysis?

a) The tendency of a sample statistic to be different from the population parameter
b) The randomness in a sample
c) The spread of data points around the mean
d) The correlation between two variables
Answer: a) The tendency of a sample statistic to be different from the population parameter

45. What is the main purpose of a hypothesis test?

a) To describe the characteristics of a dataset
b) To estimate population parameters
c) To determine whether there is enough evidence to reject a null hypothesis
d) To identify patterns in data
Answer: c) To determine whether there is enough evidence to reject a null hypothesis

46. What is the main difference between parametric and non-parametric tests?

a) Parametric tests assume normality, while non-parametric tests do not
b) Non-parametric tests are more powerful than parametric tests
c) Parametric tests are used for categorical data, while non-parametric tests are used for continuous data
d) Non-parametric tests assume homoscedasticity, while parametric tests do not
Answer: a) Parametric tests assume normality, while non-parametric tests do not

47. In a box plot, what do the “whiskers” represent?

a) The range of the data
b) The interquartile range
c) The median of the data
d) The mean of the data
Answer: a) The range of the data

48. What does the term “regression coefficient” represent?

a) The relationship between two variables
b) The intercept of the regression line
c) The slope of the regression line
d) The residuals of the regression model
Answer: c) The slope of the regression line

49. What is the purpose of a likelihood ratio test?

a) To test the fit of a statistical model
b) To compare the means of two groups
c) To test the significance of individual predictors in a regression model
d) To estimate population parameters
Answer: a) To test the fit of a statistical model

50. What is a “confounding variable”?

a) A variable that is not included in the model but affects the dependent variable
b) A variable that is measured but not used in the analysis
c) A variable that is the main focus of the study
d) A variable that has no effect on the dependent variable
Answer: a) A variable that is not included in the model but affects the dependent variable

51. What does the term “normality” refer to in statistical analysis?

a) The distribution of data follows a normal distribution
b) The spread of data points around the mean
c) The relationship between two variables
d) The central tendency of a dataset
Answer: a) The distribution of data follows a normal distribution

52. What is the main purpose of a Q-Q plot?

a) To compare the means of two groups
b) To assess if a dataset follows a normal distribution
c) To test the significance of regression coefficients
d) To monitor the stability of a process over time
Answer: b) To assess if a dataset follows a normal distribution

53. Which of the following is a type of non-parametric test?

a) t-test
b) ANOVA
c) Wilcoxon signed-rank test
d) Regression analysis
Answer: c) Wilcoxon signed-rank test

54. What does the term “degrees of freedom” refer to in statistical testing?

a) The number of independent values in a calculation
b) The number of samples in a dataset
c) The number of variables in a model
d) The number of observations in a sample
Answer: a) The number of independent values in a calculation

55. What is the main purpose of data transformation in statistical analysis?

a) To summarize the main features of a dataset
b) To make the data more suitable for analysis
c) To test the significance of relationships between variables
d) To calculate the mean and variance of a dataset
Answer: b) To make the data more suitable for analysis

56. What does “autocorrelation” refer to in time series analysis?

a) The correlation of a time series with its own past values
b) The correlation between two different time series
c) The correlation of residuals in regression analysis
d) The correlation of a variable with a categorical outcome
Answer: a) The correlation of a time series with its own past values

57. What is the main difference between a parametric and a non-parametric test?

a) Parametric tests assume a specific distribution for the data, while non-parametric tests do not
b) Non-parametric tests are used for large sample sizes, while parametric tests are used for small samples
c) Parametric tests are always more accurate than non-parametric tests
d) Non-parametric tests require data to be normally distributed, while parametric tests do not
Answer: a) Parametric tests assume a specific distribution for the data, while non-parametric tests do not

58. What is the primary use of a histogram?

a) To show the distribution of a dataset
b) To compare the means of two groups
c) To display the relationship between two variables
d) To test the significance of a hypothesis
Answer: a) To show the distribution of a dataset

59. What does a high correlation coefficient indicate?

a) No relationship between two variables
b) A strong relationship between two variables
c) A weak relationship between two variables
d) A significant difference between two means
Answer: b) A strong relationship between two variables

60. What does the term “effect size” indicate in statistical analysis?

a) The degree to which a result is statistically significant
b) The magnitude of the observed effect or difference
c) The probability of making a Type I error
d) The spread of data around the mean
Answer: b) The magnitude of the observed effect or difference

61. In statistical terms, what is “power”?

a) The probability of making a Type II error
b) The probability of rejecting a false null hypothesis
c) The probability of accepting a true null hypothesis
d) The significance level of a test
Answer: b) The probability of rejecting a false null hypothesis

62. What does “homoscedasticity” refer to in regression analysis?

a) The constant variance of residuals across levels of the independent variable
b) The normal distribution of residuals
c) The relationship between two independent variables
d) The correlation of residuals with past values
Answer: a) The constant variance of residuals across levels of the independent variable

63. What is a “sensitivity analysis” used for in statistical modeling?

a) To determine how changes in inputs affect the outputs of a model
b) To assess the normality of residuals
c) To compare the means of two groups
d) To test the significance of regression coefficients
Answer: a) To determine how changes in inputs affect the outputs of a model

64. What does the term “residual” refer to in regression analysis?

a) The difference between observed and predicted values
b) The value of the dependent variable
c) The intercept of the regression line
d) The correlation between two variables
Answer: a) The difference between observed and predicted values

65. What is the purpose of a principal component analysis (PCA)?

a) To reduce the dimensionality of a dataset while preserving as much variance as possible
b) To compare the means of different groups
c) To test the significance of regression coefficients
d) To analyze the distribution of a single variable
Answer: a) To reduce the dimensionality of a dataset while preserving as much variance as possible

66. What does the term “outlier” refer to in statistical analysis?

a) A data point that significantly differs from the rest of the data
b) A data point that is missing from the dataset
c) A data point that is close to the mean
d) A data point that is irrelevant to the analysis
Answer: a) A data point that significantly differs from the rest of the data

67. What is the main goal of multivariate analysis?

a) To analyze the relationship between multiple variables simultaneously
b) To summarize the characteristics of a single variable
c) To test the significance of differences between two groups
d) To compare the means of different groups
Answer: a) To analyze the relationship between multiple variables simultaneously

68. What is the purpose of a p-value in hypothesis testing?

a) To measure the strength of the evidence against the null hypothesis
b) To estimate the population parameter
c) To calculate the sample mean
d) To assess the variability within a sample
Answer: a) To measure the strength of the evidence against the null hypothesis

69. What does “statistical significance” mean?

a) The result is unlikely to have occurred by chance
b) The result is important in practical terms
c) The result shows a large effect size
d) The result is not influenced by outliers
Answer: a) The result is unlikely to have occurred by chance

70. What is a “Type II error” in hypothesis testing?

a) Failing to reject a false null hypothesis
b) Rejecting a true null hypothesis
c) Accepting an alternative hypothesis
d) Not detecting a true effect
Answer: a) Failing to reject a false null hypothesis

71. What does “model fit” refer to in statistical modeling?

a) How well the model explains the observed data
b) The number of parameters in the model
c) The complexity of the model
d) The statistical significance of the model
Answer: a) How well the model explains the observed data

72. What is the purpose of the Kolmogorov-Smirnov test?

a) To test if a sample follows a specific distribution
b) To compare the means of two groups
c) To test the significance of regression coefficients
d) To assess the homogeneity of variances
Answer: a) To test if a sample follows a specific distribution

73. What does “mean” refer to in statistical terms?

a) The average value of a dataset
b) The most frequent value in a dataset
c) The middle value of a dataset
d) The spread of values around the mean
Answer: a) The average value of a dataset

74. What is the purpose of a “t-test for paired samples”?

a) To compare the means of two related groups
b) To compare the means of two independent groups
c) To test the correlation between two variables
d) To analyze the variance within a single group
Answer: a) To compare the means of two related groups

75. What does the term “variance” measure in statistics?

a) The spread or dispersion of a set of values
b) The average value of a dataset
c) The most frequent value in a dataset
d) The correlation between two variables
Answer: a) The spread or dispersion of a set of values

76. What is the main focus of logistic regression?

a) To model the probability of a binary outcome
b) To compare the means of different groups
c) To analyze the variance within a dataset
d) To describe the distribution of a single variable
Answer: a) To model the probability of a binary outcome

77. What does the term “sampling distribution” refer to?

a) The distribution of a sample statistic over many samples
b) The distribution of data within a single sample
c) The distribution of a population parameter
d) The distribution of errors in a model
Answer: a) The distribution of a sample statistic over many samples

78. What is a “normal probability plot” used for?

a) To assess if data follows a normal distribution
b) To compare the means of two groups
c) To test the significance of regression coefficients
d) To monitor the stability of a process over time
Answer: a) To assess if data follows a normal distribution

79. What is the primary goal of a data visualization?

a) To communicate information clearly and effectively
b) To calculate statistical measures
c) To perform hypothesis testing
d) To compare different statistical models
Answer: a) To communicate information clearly and effectively

80. What does “autocorrelation” measure in time series analysis?

a) The correlation of a time series with its own past values
b) The correlation between two different time series
c) The correlation of residuals in regression analysis
d) The correlation between two variables in a dataset
Answer: a) The correlation of a time series with its own past values

Statistics for Business Analytics

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