Computational statistics

1. Computational statistics is a branch of statistics that focuses on the methods and techniques for analyzing data using computational tools and algorithms. It involves the development and application of statistical models, simulations, and algorithms to analyze and interpret complex datasets. Computational statistics plays a crucial role in various fields such as machine learning, data science, bioinformatics, and image analysis, providing researchers and analysts with the necessary tools to extract meaningful insights from large and complex datasets. By combining statistical theory with computer science techniques, computational statistics enables practitioners to efficiently and accurately analyze data, explore patterns and trends, and make informed decisions based on statistical inference and predictive modeling.

What is a p-value in hypothesis testing?

A) The measure of confidence in the null hypothesis
B) The population parameter being tested
C) The significance level for accepting the null hypothesis
D) The probability of obtaining results at least as extreme as the observed results, given that the null hypothesis is true

2. Which of the following is a parametric statistical test?

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

3. What is the purpose of regression analysis in statistics?

A) To test for differences in means
B) To examine the relationship between variables
C) To summarize categorical data
D) To identify outliers in a dataset

4. What does the correlation coefficient measure?

A) The strength and direction of a linear relationship between two variables
B) The spread of the data
C) The central tendency of a dataset
D) The variability within groups

5. What is the purpose of a confidence interval in statistics?

A) To determine the probability of an event occurring
B) To estimate the range within which the population parameter is likely to fall
C) To predict future data points
D) To compare two independent groups

6. Which type of sampling technique involves randomly selecting subjects from a population?

A) Convenience sampling
B) Systematic sampling
C) Cluster sampling
D) Simple random sampling

7. In statistical hypothesis testing, what is the null hypothesis?

A) The hypothesis that is tested using a one-tailed test
B) The hypothesis that the researcher believes to be true
C) A statement that there is no significant difference between specified populations
D) A statement that predicts an outcome in an experiment

8. What is the difference between correlation and causation?

A) Correlation measures the strength of a relationship, while causation measures the direction
B) Correlation is used for categorical data, while causation is used for continuous data
C) Correlation indicates a relationship between variables, while causation implies one variable causes a change in the other
D) Correlation refers to linear relationships, while causation refers to non-linear relationships

9. What is the purpose of the Central Limit Theorem in statistics?

A) To compare two different samples
B) To calculate the range of a dataset
C) To determine the variability within groups
D) To state that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases

10. What is the significance level in hypothesis testing?

A) The level of confidence in the alternative hypothesis
B) The probability of rejecting the null hypothesis when it is actually true
C) The measure of correlation between two variables
D) The margin of error in the sample mean

11. Which statistical test should be used to compare the means of more than two independent groups?

A) ANOVA
B) T-test
C) Regression analysis
D) Chi-square test

12. Which statistical technique is used to predict the value of a dependent variable based on one or more independent variables?

A) Time series analysis.
B) Factor analysis.
C) Cluster analysis.
D) Regression analysis.

13. Which regression technique is used when the dependent variable is binary?

A) Polynomial regression.
B) Linear regression.
C) Logistic regression.
D) Ridge regression.

14. Which statistical test is used to determine if there is a significant association between two categorical variables?

A) T-test.
B) ANOVA.
C) Regression analysis.
D) Chi-square test.

15. Which statistical technique is used to deal with missing values in a dataset?

A) Outlier detection.
B) Imputation.
C) Feature engineering.
D) Normalization.

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