Statistical theory

1. Statistical theory is a branch of mathematics that deals with the analysis, interpretation, and presentation of data. It involves various techniques and methods for summarizing and making inferences about a population based on sample data. Key concepts in statistical theory include probability distributions, hypothesis testing, regression analysis, and more. The goal of statistical theory is to provide a framework for understanding uncertainty and variability in data, enabling us to draw meaningful conclusions and make informed decisions in various fields such as science, business, and social sciences.

What is the purpose of hypothesis testing in statistics?

A) To calculate the probability of an event.
B) To visualize data using graphs.
C) To determine if there is enough evidence to reject a null hypothesis.
D) To summarize data using summary statistics.

2. What is the Central Limit Theorem?

A) States that the sampling distribution of the sample means approaches a normal distribution as the sample size increases.
B) A method for outlier detection in data.
C) Describes the spread of data points in a dataset.
D) A type of statistical hypothesis testing.

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

A) A type of data transformation.
B) When the null hypothesis is not rejected, but it is false.
C) A calculation error in statistical analysis.
D) When the null hypothesis is rejected, but it is actually true.

4. What is a Type II error in hypothesis testing?

A) A statistical measure of association.
B) A type of sampling technique.
C) When the null hypothesis is not rejected, but it is actually false.
D) When the null hypothesis is rejected, and it is true.

5. What is correlation in statistics?

A) The probability of an event occurring.
B) The difference between the maximum and minimum values in a dataset.
C) A type of data visualization technique.
D) A measure of the strength and direction of a linear relationship between two variables.

6. What is regression analysis used for in statistics?

A) To calculate the median value of a dataset.
B) To summarize data using descriptive statistics.
C) To determine the mode of a distribution.
D) To analyze the relationship between a dependent variable and one or more independent variables.

7. What is the formula for variance in statistics?

A) The sum of all data values divided by the number of values.
B) The range of values in a dataset.
C) The middle value in a set of ordered data points.
D) The average of the squared differences from the mean.

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

A) Mean
B) Correlation Coefficient
C) Standard Deviation
D) Variance

9. What is the mode of a dataset?

A) The value that appears most frequently in the dataset.
B) The average of all values in the dataset.
C) The middle value in a sorted dataset.
D) The difference between the maximum and minimum values.

10. What is the range of a dataset?

A) The average of all values in the dataset.
B) The difference between the maximum and minimum values in the dataset.
C) The number of values in the dataset.
D) The sum of all values in the dataset.

11. What is a percentile in statistics?

A) The variance of a dataset.
B) A value below which a given percentage of observations in a group falls.
C) The average of all data points in a dataset.
D) The range of values in a dataset.

12. Which of the following is a non-parametric statistical test?

A) Mann-Whitney U test
B) Regression analysis
C) ANOVA
D) T-test

13. What is the null hypothesis in hypothesis testing?

A) A statement that there is no significant difference or relationship between variables.
B) A conclusion drawn from statistical analysis.
C) A measure of the strength of a relationship.
D) A statement that a significant difference exists between variables.

14. Which statistical test is used to compare the means of more than two groups?

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

15. Which statistical test is used to determine if there is a significant difference between the means of two groups?

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

16. What does skewness measure in a dataset?

A) The degree of asymmetry in the distribution of data.
B) The presence of outliers in the dataset.
C) The spread of data points from the mean.
D) The relationship between two variables.

17. What is a chi-square test used for in statistics?

A) To calculate the correlation coefficient.
B) To determine if there is a significant association between two categorical variables.
C) To analyze the relationship between a dependent and an independent variable.
D) To find the median value of a dataset.

18. What is statistical power in hypothesis testing?

A) The probability of rejecting a false null hypothesis.
B) The confidence interval for a parameter estimate.
C) The significance level for hypothesis testing.
D) The strength of the relationship between variables.

19. Which type of bias occurs when some groups in a population are systematically left out of a study?

A) Sampling bias
B) Response bias
C) Selection bias
D) Measurement bias

20. What is a box plot used for in statistics?

A) To test for correlations between variables.
B) To calculate the average value of a dataset.
C) To visualize the distribution of a dataset and identify outliers.
D) To calculate confidence intervals.

21. In a normal distribution, what percentage of data points fall within one standard deviation of the mean?

A) 99.7%
B) 68%
C) 95%
D) 50%

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

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

23. What term is used to describe the measure of the spread of values in a dataset?

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

24. What is the standard deviation?

A) A measure of the dispersion of data points around the mean.
B) The maximum value in the dataset.
C) The average of all values in the dataset.
D) The middle value in a sorted dataset.

25. What is probability sampling?

A) A non-statistical method of gathering data.
B) A sampling technique that relies on random selection of individuals.
C) A sampling technique that selects individuals based on convenience.
D) A sampling technique where each member of the population has a known and non-zero chance of being selected into the sample.

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