CSS Statistics MCQs

This comprehensive set of MCQs on Statistics for the Central Superior Services (CSS) examination is tailored to cover all fundamental topics outlined in the CSS Statistics syllabus. Encompassing essential areas such as Descriptive Statistics, Probability Theory, Inferential Statistics, Sampling Techniques, and Data Analysis, these MCQs are designed to help CSS candidates build a strong foundation in statistical concepts and applications.

Who should practice CSS Statistics MCQs?

Candidates preparing for the CSS examination who aim to strengthen their understanding of statistical methods and data interpretation skills.
Individuals seeking to enhance their knowledge of probability, hypothesis testing, and regression analysis, crucial for analytical roles in civil services.
University students focused on high-yield topics like correlation, distribution theories, and statistical inference, essential for the CSS Statistics syllabus.
Anyone looking to refine their analytical and quantitative reasoning abilities for application in research, policy-making, and data-driven decision-making.
Students committed to mastering statistical concepts that will support them in excelling in competitive exams and advancing their data literacy.

1. What is the primary purpose of descriptive statistics?

A) To summarize data
B) To predict future outcomes
C) To test hypotheses
D) To classify variables

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2. Which type of statistics involves making inferences from a sample to a population?

A) Descriptive Statistics
B) Inferential Statistics
C) Data Analysis
D) Probability Theory

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3. In statistics, what is a stem-and-leaf diagram primarily used for?

A) Summarizing categorical data
B) Displaying the shape of a data set
C) Calculating central tendency
D) Assessing correlation

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4. Which of the following is a measure of central tendency?

A) Variance
B) Mean
C) Standard Deviation
D) Range

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5. The extent to which data points differ from the mean is called:

A) Central Tendency
B) Variability
C) Probability
D) Skewness

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6. What type of plot is used to summarize the distribution of a data set, highlighting quartiles and outliers?

A) Histogram
B) Scatterplot
C) Box and Whisker Plot
D) Line Graph

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7. Which measure shows the amount of asymmetry in a distribution?

A) Variance
B) Skewness
C) Standard Deviation
D) Mean

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8. The additive law of probability states that the probability of the union of two mutually exclusive events is equal to:

A) The product of their probabilities
B) The sum of their probabilities
C) Zero
D) One

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9. If two events A and B are independent, the probability of their intersection is given by:

A) P(A) + P(B)
B) P(A) * P(B)
C) P(A | B)
D) P(A) / P(B)

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10. Bayes’ theorem is used for:

A) Calculating marginal probabilities
B) Finding conditional probabilities
C) Determining skewness
D) Estimating central tendency

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11. What do we call a variable that can take on a finite number of values?

A) Continuous Random Variable
B) Discrete Random Variable
C) Constant Variable
D) Mean Variable

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12. The expected value of a random variable is also known as its:

A) Mean
B) Median
C) Mode
D) Range

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13. Which distribution is used to model the number of successes in a fixed number of trials?

A) Normal Distribution
B) Binomial Distribution
C) Poisson Distribution
D) Exponential Distribution

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14. The standard normal distribution has a mean of:

A) 1
B) 0
C) 10
D) -1

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15. The correlation coefficient ranges between:

A) -2 and 2
B) -1 and 1
C) 0 and 1
D) 1 and 2

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16. Which non-parametric test is used to compare two related samples?

A) Sign Test
B) ANOVA
C) Chi-Square Test
D) T-Test

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17. Sampling in which each member of the population has an equal chance of selection is called:

A) Stratified Sampling
B) Simple Random Sampling
C) Cluster Sampling
D) Convenience Sampling

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18. The Central Limit Theorem states that as sample size increases, the sampling distribution of the sample mean:

A) Becomes more skewed
B) Approaches a normal distribution
C) Stays the same
D) Becomes bimodal

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19. In hypothesis testing, a Type I error occurs when:

A) The null hypothesis is incorrectly accepted
B) The alternative hypothesis is incorrectly rejected
C) The null hypothesis is incorrectly rejected
D) No errors occur

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20. The Mann-Whitney test is used when comparing:

A) Means of two independent samples
B) Variances of two samples
C) Means of related samples
D) Proportions

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21. Which of the following is a property of a good estimator?

A) It should be biased
B) It should be consistent
C) It should be complex
D) It should be time-consuming

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22. What is the purpose of interval estimation?

A) To provide a single value estimate
B) To calculate sample size
C) To give a range of plausible values for a population parameter
D) To summarize data

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23. In hypothesis testing, the null hypothesis typically states that there is:

A) No effect or no difference
B) A significant effect or difference
C) A certain probability
D) A constant variance

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24. What does a p-value represent in hypothesis testing?

A) Probability of Type I error
B) Probability of Type II error
C) The strength of evidence against the null hypothesis
D) The sample size

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25. When testing for independence in contingency tables, which test is commonly used?

A) T-Test
B) Chi-Square Test
C) ANOVA
D) Regression Analysis

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26. What is the main purpose of the analysis of variance (ANOVA)?

A) To test differences between two means
B) To compare means of three or more groups
C) To estimate a population parameter
D) To calculate probabilities

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27. Which sampling technique involves dividing the population into subgroups and then randomly selecting from these subgroups?

A) Simple Random Sampling
B) Stratified Sampling
C) Systematic Sampling
D) Cluster Sampling

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28. In a two-way ANOVA, what is being analyzed?

A) One independent variable
B) Two dependent variables
C) Two or more independent variables
D) A single dependent variable

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29. A common method for comparing means of different treatments in an experiment is:

A) T-Test
B) Chi-Square Test
C) ANOVA
D) Regression

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30. What is a primary advantage of using non-parametric tests?

A) They require a larger sample size
B) They can be used with non-normal distributions
C) They are always more powerful than parametric tests
D) They require homogeneity of variances

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31. The term “blocking” in experimental design refers to:

A) Randomly assigning subjects
B) Grouping similar experimental units
C) Analyzing variance
D) Testing hypotheses

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32. The variance is a measure of:

A) Central tendency
B) Dispersion
C) Skewness
D) Correlation

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33. A significant result in hypothesis testing indicates:

A) The null hypothesis is true
B) The alternative hypothesis is likely true
C) No difference exists
D) There is a sampling error

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34. Which test would you use for analyzing data when the sample sizes are small and the population variance is unknown?

A) T-Test
B) Z-Test
C) Chi-Square Test
D) ANOVA

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35. The mean of a discrete random variable can be calculated using:

A) Sum of all values divided by the number of values
B) The probability distribution
C) Standard deviation
D) Variance

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36. Which of the following distributions is commonly used to model rare events?

A) Binomial Distribution
B) Poisson Distribution
C) Normal Distribution
D) Uniform Distribution

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37. What is the shape of a normal distribution?

A) Skewed
B) Uniform
C) Bell-shaped
D) Rectangular

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38. In regression analysis, the method of least squares is used to:

A) Minimize the sum of absolute errors
B) Maximize the correlation coefficient
C) Minimize the sum of squared differences between observed and predicted values
D) Calculate the mean

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39. Which of the following is a key assumption of linear regression?

A) The relationship between variables is non-linear
B) Residuals are normally distributed
C) Independent variables are highly correlated
D) Dependent variable is categorical

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40. What does a correlation coefficient of 0 indicate?

A) Perfect positive correlation
B) Perfect negative correlation
C) No correlation
D) Strong correlation

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41. What does the term “statistical independence” imply?

A) Two events are related
B) The occurrence of one event does not affect the other
C) Both events have the same probability
D) Events are mutually exclusive

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42. Which of the following sampling methods selects every nth individual from a population?

A) Simple Random Sampling
B) Systematic Sampling
C) Stratified Sampling
D) Cluster Sampling

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43. In a Box and Whisker plot, the line inside the box represents:

A) The median
B) The mean
C) The range
D) The interquartile range

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44. Which type of graph is best for showing the distribution of a continuous variable?

A) Bar Chart
B) Pie Chart
C) Histogram
D) Line Graph

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45. What is the main purpose of descriptive statistics?

A) To make inferences about a population
B) To summarize and describe data
C) To establish causality
D) To analyze relationships between variables

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46. What does the stem-and-leaf diagram primarily display?

A) The frequency of data
B) The shape of the distribution
C) Both the shape and the distribution of data
D) Only the median

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47. In statistics, what does the term “kurtosis” refer to?

A) The measure of central tendency
B) The measure of dispersion
C) The shape of the distribution
D) The relationship between two variables

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48. The additive law of probability is used to find the probability of:

A) Independent events
B) Mutually exclusive events
C) Dependent events
D) Conditional events

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49. If two events are mutually exclusive, which of the following is true?

A) They can occur at the same time
B) The probability of both events occurring together is greater than zero
C) The probability of either event occurring is the sum of their individual probabilities
D) They are independent events

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50. The normal approximation to the binomial distribution is applicable when:

A) Sample size is very small
B) Number of trials is large and probability of success is neither very small nor very large
C) The sample size is less than 30
D) Success probability is 0.5

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51. What is the primary characteristic of a discrete random variable?

A) Can take any value in an interval
B) Can only take specific values
C) Is always continuous
D) Is unbounded

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52. Which of the following distributions is used for modeling the number of successes in a fixed number of independent Bernoulli trials?

A) Normal Distribution
B) Binomial Distribution
C) Poisson Distribution
D) Uniform Distribution

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53. Which test is used to assess the goodness of fit of observed data to a theoretical distribution?

A) Z-Test
B) Chi-Square Test
C) T-Test
D) ANOVA

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54. In regression analysis, the dependent variable is also known as:

A) Predictor variable
B) Independent variable
C) Response variable
D) Control variable

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55. What does a correlation coefficient of +1 indicate?

A) Perfect negative correlation
B) No correlation
C) Perfect positive correlation
D) Weak positive correlation

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56. What is a “null hypothesis” in hypothesis testing?

A) A statement of no effect or no difference
B) A statement that there is an effect
C) A complex theory
D) A statement about the population variance

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57. When performing a t-test, which assumption must be met?

A) Sample size must be at least 30
B) Samples must be independent
C) Variances of both groups must be unequal
D) Populations must be non-normal

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58. Which sampling method involves selecting groups of individuals rather than individuals themselves?

A) Simple Random Sampling
B) Stratified Sampling
C) Cluster Sampling
D) Systematic Sampling

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59. In hypothesis testing, a Type I error occurs when:

A) The null hypothesis is accepted when it is false
B) The null hypothesis is rejected when it is true
C) The alternative hypothesis is accepted when it is false
D) The sample size is too small

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60. The central limit theorem states that:

A) The means of samples will be normally distributed, regardless of the population distribution
B) The variance of a sample will equal the population variance
C) All populations are normally distributed
D) A larger sample size leads to greater variability

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61. Which of the following is NOT a non-parametric test?

A) Mann-Whitney U test
B) Wilcoxon signed-rank test
C) T-test
D) Kruskal-Wallis test

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62. The method of least squares is primarily used for:

A) Calculating probabilities
B) Estimating the parameters of a regression model
C) Conducting hypothesis tests
D) Analyzing variance

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63. What is the main purpose of a contingency table?

A) To display frequencies of two categorical variables
B) To show trends over time
C) To display the distribution of a single variable
D) To summarize quantitative data

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64. Which of the following is an assumption of ANOVA?

A) Observations are independent
B) All groups have equal variances
C) Data are normally distributed
D) All of the above

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65. In a normal distribution, what percentage of the data lies within one standard deviation of the mean?

A) 50%
B) 68%
C) 95%
D) 99%

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66. Which measure is used to describe the average of a set of values?

A) Median
B) Mode
C) Range
D) Mean

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67. A sample that is selected based on the convenience of the researcher is called:

A) Random Sample
B) Stratified Sample
C) Quota Sample
D) Convenience Sample

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68. Which of the following tests compares the medians of two related samples?

A) Independent t-test
B) Wilcoxon signed-rank test
C) Chi-square test
D) Paired t-test

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69. In a probability distribution, the mean of a discrete random variable is defined as:

A) The most frequently occurring value
B) The sum of all possible values multiplied by their probabilities
C) The median of the distribution
D) The difference between the maximum and minimum values

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70. The primary goal of regression analysis is to:

A) Describe the variability in the data
B) Establish causation between variables
C) Predict the value of a dependent variable based on independent variables
D) Summarize the characteristics of a sample

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71. Which type of sampling technique ensures that every member of the population has an equal chance of being selected?

A) Stratified Sampling
B) Convenience Sampling
C) Simple Random Sampling
D) Systematic Sampling

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72. The coefficient of determination (R²) indicates:

A) The percentage of variation in the dependent variable explained by the independent variable(s)
B) The strength of the correlation between two variables
C) The goodness of fit of the regression model
D) All of the above

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73. The mode is defined as:

A) The average of a data set
B) The middle value in a sorted list
C) The most frequently occurring value in a data set
D) The difference between the maximum and minimum values

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74. What does the term “statistical significance” indicate?

A) The results are due to chance
B) The results are important in a practical sense
C) The results are unlikely to have occurred by chance
D) The sample size is large

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75. Which of the following is NOT a characteristic of the normal distribution?

A) Symmetrical about the mean
B) Mean, median, and mode are equal
C) Has a single peak
D) It is skewed

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76. In hypothesis testing, a Type II error occurs when:

A) The null hypothesis is rejected when it is true
B) The null hypothesis is accepted when it is false
C) The alternative hypothesis is accepted when it is false
D) The sample size is too small

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77. Which of the following is a property of the binomial distribution?

A) The number of trials is infinite
B) Each trial is dependent on the previous trial
C) There are only two possible outcomes for each trial
D) The probabilities of outcomes change with each trial

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78. Which test is appropriate for testing the difference between the means of two independent samples?

A) Paired t-test
B) ANOVA
C) Independent t-test
D) Chi-square test

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79. The variance of a random variable is a measure of:

A) Central tendency
B) Data dispersion
C) Skewness
D) Kurtosis

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80. Which of the following is an example of a discrete probability distribution?

A) Normal Distribution
B) Exponential Distribution
C) Poisson Distribution
D) Uniform Distribution

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81. The purpose of conducting a goodness-of-fit test is to:

A) Compare the means of two populations
B) Determine how well a statistical model fits the observed data
C) Assess the relationship between two variables
D) Estimate the population parameters

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82. Which of the following is a non-parametric test for two independent samples?

A) Independent t-test
B) Mann-Whitney U test
C) Paired t-test
D) ANOVA

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83. In a box-and-whisker plot, the box represents:

A) The range of the data
B) The interquartile range (IQR)
C) The median only
D) The maximum and minimum values

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84. If a dataset is positively skewed, which of the following is true?

A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mean = Mode > Median

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85. The Central Limit Theorem states that:

A) The sample mean is always equal to the population mean
B) The distribution of the sample means approaches a normal distribution as sample size increases
C) All populations are normally distributed
D) The variance of a sample is equal to the variance of the population

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86. The critical value in hypothesis testing is used to:

A) Determine the sample size
B) Identify the region of acceptance or rejection for the null hypothesis
C) Calculate the mean of the sample
D) Estimate the population variance

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87. In multiple regression analysis, the term “multicollinearity” refers to:

A) The linear relationship between the dependent and independent variables
B) The correlation between independent variables
C) The relationship between the dependent variable and one independent variable
D) The error term in the regression equation

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88. The range of a dataset is defined as:

A) The difference between the highest and lowest values
B) The average of the values
C) The middle value of the sorted data
D) The most frequently occurring value

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89. Which of the following sampling techniques divides the population into subgroups and then randomly samples from each subgroup?

A) Simple Random Sampling
B) Stratified Sampling
C) Systematic Sampling
D) Cluster Sampling

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90. What is the purpose of a chi-square test?

A) To compare means of two populations
B) To assess relationships between categorical variables
C) To test for normality in a dataset
D) To calculate correlation coefficients

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91. A variable that can take on an infinite number of values within a given range is known as:

A) Discrete Variable
B) Continuous Variable
C) Nominal Variable
D) Ordinal Variable

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92. In hypothesis testing, what does the p-value represent?

A) The probability that the null hypothesis is true
B) The probability of observing the data if the null hypothesis is true
C) The probability of making a Type I error
D) The significance level of the test

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93. Which of the following is a property of the Poisson distribution?

A) It models the number of events in a fixed interval of time or space
B) It is symmetrical
C) It has a fixed mean and variance equal to 1
D) It applies to continuous random variables

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94. When conducting a hypothesis test, the null hypothesis typically states:

A) There is an effect or difference
B) There is no effect or difference
C) The alternative hypothesis is true
D) The sample is representative of the population

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95. The term “statistical power” refers to:

A) The likelihood of making a Type I error
B) The probability of correctly rejecting the null hypothesis when it is false
C) The strength of the relationship between variables
D) The effect size of a statistical test

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96. In a linear regression equation, the slope represents:

A) The expected change in the dependent variable for a one-unit change in the independent variable
B) The value of the dependent variable when the independent variable is zero
C) The average value of the dependent variable
D) The correlation between the independent and dependent variables

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97. What is the primary use of sampling techniques in statistics?

A) To reduce the size of the population
B) To make inferences about the population from a subset of data
C) To eliminate bias in data collection
D) To increase the accuracy of the results

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98. The F-distribution is commonly used in which type of statistical analysis?

A) Regression Analysis
B) Analysis of Variance (ANOVA)
C) Chi-square Tests
D) Non-parametric Tests

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99. Which of the following is a characteristic of the standard normal distribution?

A) Mean is greater than median
B) Standard deviation is equal to 1
C) It is skewed to the right
D) It has multiple peaks

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100. In statistics, the term “kurtosis” refers to:

A) The measure of central tendency
B) The measure of variability
C) The shape of the distribution, particularly its tails
D) The correlation between two variables

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