Đề thi, bài tập trắc nghiệm online Lý thuyết xác suất và thống kê – Đề 13

1. In regression analysis, what does the R-squared value represent?

A. The slope of the regression line.

B. The intercept of the regression line.

C. The proportion of variance in the dependent variable that is predictable from the independent variable(s).

D. The standard error of the regression model.

2. What is the difference between independent and dependent events in probability?

A. Independent events cannot happen at the same time, while dependent events must happen at the same time.

B. Independent events affect each other's probabilities, while dependent events do not.

C. Independent events do not affect each other's probabilities, while dependent events do.

D. Independent events are always more likely than dependent events.

3. Which of the following distributions is often used to model the number of events occurring in a fixed interval of time or space?

A. Normal distribution

B. Binomial distribution

C. Poisson distribution

D. Uniform distribution

4. What is the correlation coefficient measuring?

A. The difference between means of two variables.

B. The strength and direction of a linear relationship between two variables.

C. The probability of causation between two variables.

D. The variance of two variables.

5. What is the fundamental difference between probability and statistics?

A. Probability deals with past events, while statistics deals with future events.

B. Probability deals with predicting the likelihood of future events based on known models, while statistics uses observed data to infer properties of underlying probability distributions.

C. Probability is a branch of mathematics, while statistics is a branch of computer science.

D. There is no difference; probability and statistics are the same discipline.

6. What is the expected value of a random variable?

A. The most likely value of the random variable.

B. The median value of the random variable.

C. The average value of the random variable over many repeated trials.

D. The value that occurs with the highest probability.

7. What is the difference between sensitivity and specificity in diagnostic testing?

A. Sensitivity is the probability of testing negative given the disease is absent, and specificity is the probability of testing positive given the disease is present.

B. Sensitivity and specificity are the same thing in diagnostic testing.

C. Sensitivity is the probability of testing positive given the disease is present, and specificity is the probability of testing negative given the disease is absent.

D. Sensitivity is the proportion of true positives among all positives, and specificity is the proportion of true negatives among all negatives.

8. Which measure of central tendency is most affected by outliers?

A. Median

B. Mode

C. Mean

D. All are equally affected.

9. Which of the following is a discrete probability distribution?

A. Normal distribution

B. Exponential distribution

C. Binomial distribution

D. Uniform distribution (continuous)

10. What is the meaning of 'statistical significance'?

A. The result is important in a practical, real-world sense.

B. The result is unlikely to have occurred by chance alone, assuming the null hypothesis is true.

C. The result is definitely true and applicable to the entire population.

D. The result is due to a large sample size.

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

A. To compare the means of two groups.

B. To analyze the variance within a single group.

C. To compare the means of three or more groups to see if at least one mean is different.

D. To analyze the correlation between two variables.

12. Which of the following scenarios best illustrates the concept of conditional probability?

A. The probability of rolling a 6 on a fair six-sided die.

B. The probability of drawing a King from a standard deck of cards.

C. The probability of rain tomorrow, given that it is cloudy today.

D. The probability of flipping heads on a fair coin.

13. What does the Central Limit Theorem state?

A. The mean of the sample is always equal to the population mean.

B. The sum of independent random variables will always follow a normal distribution.

C. The distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

D. The variance of the sample is always equal to the population variance.

14. What does standard deviation measure?

A. The central tendency of a dataset.

B. The probability of an event occurring.

C. The spread or dispersion of data points around the mean.

D. The correlation between two variables.

15. What is the difference between a Type I error and a Type II error in hypothesis testing?

A. Type I error is failing to reject a false null hypothesis, and Type II error is rejecting a true null hypothesis.

B. Type I error is rejecting a true null hypothesis, and Type II error is failing to reject a false null hypothesis.

C. Type I error occurs when the sample size is too small, and Type II error occurs when the sample size is too large.

D. Type I error is made in parametric tests, and Type II error is made in non-parametric tests.

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

A. Mean

B. Median

C. Range

D. Mode

17. What is multicollinearity in regression analysis?

A. When the dependent variable is correlated with itself.

B. When independent variables are highly correlated with each other.

C. When the error terms in the regression model are correlated.

D. When there are multiple dependent variables in the model.

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

A. T-test

B. ANOVA

C. Chi-square test

D. Regression analysis

19. What is a random variable?

A. A variable whose value is fixed and known with certainty.

B. A variable whose value is a numerical outcome of a random phenomenon.

C. A variable that can only take on integer values.

D. A variable that is used to represent the sample space.

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

A. To determine the probability that the null hypothesis is true.

B. To measure the effect size of the findings.

C. To indicate the strength of evidence against the null hypothesis.

D. To set the significance level of the test.

21. What is the purpose of a confidence interval?

A. To estimate the probability of a specific sample statistic.

B. To provide a range of values that is likely to contain the true population parameter.

C. To determine the exact value of a population parameter.

D. To test a hypothesis about a population parameter.

22. What is the difference between population and sample?

A. Population is a subset of the sample.

B. Sample is the entire group we want to know about, and population is a subset of it.

C. Population is the entire group we want to know about, and sample is a subset of the population from which we collect data.

D. Population and sample are always the same.

23. What is the law of large numbers?

A. The average of the results obtained from a large number of trials should be close to the expected value.

B. Larger samples always lead to larger sample means.

C. The probability of rare events increases with more trials.

D. Sample variance always increases with sample size.

24. What is the purpose of stratified sampling?

A. To ensure every individual in the population has an equal chance of being selected.

B. To reduce bias by selecting participants randomly.

C. To divide the population into subgroups (strata) and then randomly sample from each stratum, ensuring representation of each subgroup.

D. To sample individuals based on their convenience and availability.

25. Which type of data is considered categorical and nominal?

A. Temperature in Celsius

B. Height in centimeters

C. Colors of cars (e.g., red, blue, green)

D. Ranking in a race (1st, 2nd, 3rd)

26. What is the purpose of bootstrapping in statistics?

A. To increase the sample size of a dataset.

B. To estimate the sampling distribution of a statistic by resampling with replacement from the original sample.

C. To reduce bias in data collection.

D. To calculate the exact probability of an event.

27. In hypothesis testing, what is the purpose of the null hypothesis?

A. To prove the research hypothesis.

B. To state what we expect to find.

C. To state the assumption of no effect or no difference, which we aim to disprove.

D. To accept it as true based on sample data.

28. Which of the following is NOT a measure of dispersion?

A. Variance

B. Standard Deviation

C. Interquartile Range

D. Median

29. Which distribution is often associated with 'waiting times' until an event occurs?

A. Normal distribution

B. Binomial distribution

C. Exponential distribution

D. Poisson distribution

30. What is the role of degrees of freedom in statistical tests?

A. To determine the sample size needed for the test.

B. To adjust for the number of parameters estimated from the data, affecting the shape of the test statistic's distribution.

C. To measure the strength of the relationship between variables.

D. To set the significance level of the test.