Đề 1 – Bài tập, đề thi trắc nghiệm online Lý thuyết xác suất và thống kê

A A. The average of the results obtained from a large number of trials should be exactly equal to the expected value. B B. As the number of trials of a random experiment increases, the sample mean approaches the population mean. C C. Larger samples always give less variable means. D D. The sum of probabilities in any experiment must equal a large number.

A A. Central tendency B B. The most frequent value C C. Dispersion or spread of data points around the mean D D. The middle value in a dataset

A A. The region where the null hypothesis is always accepted. B B. The set of values of the test statistic for which the null hypothesis is rejected. C C. The region around the sample mean. D D. The region where the p-value is always greater than the significance level.

A A. To make the sample size larger. B B. To ensure every individual in the population has an equal chance of being selected. C C. To reduce sampling error by dividing the population into homogeneous subgroups (strata) and then sampling from each stratum. D D. To introduce bias into the sample for specific research purposes.

A A. Type II error B B. Standard error C C. Type I error D D. Sampling error

A A. Any real number B B. 0 to infinity C C. -1 to 1 D D. 0 to 1

A A. The hypothesis that the researcher is trying to prove. B B. A statement of no effect or no difference, which is tested against the alternative hypothesis. C C. The hypothesis that is always true. D D. The hypothesis based on sample data.

A A. Standard deviation is the square of the variance. B B. Variance is the square root of the standard deviation. C C. Standard deviation is the square root of the variance. D D. They are unrelated measures.

A A. They cannot occur at the same time. B B. The occurrence of one event affects the probability of the other event. C C. The occurrence of one event does not affect the probability of the other event. D D. They are mutually exclusive.

A A. Mean < Median < Mode B B. Mode < Median < Mean C C. Mean = Median = Mode D D. Median < Mode < Mean

A A. Calculating the probability of independent events. B B. Updating probabilities based on new evidence. C C. Finding the mean of a distribution. D D. Determining the variance of a distribution.

A A. Height of a person B B. Temperature of a room C C. Number of cars passing a point on a highway in an hour D D. Time taken to complete a race

A A. To ensure the sample is exactly the same as the population. B B. To introduce bias into the sample. C C. To minimize bias and ensure the sample is representative of the population, allowing for valid inferences. D D. To make the sample smaller and easier to manage.

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

A A. To estimate the exact population parameter. B B. To provide a range of plausible values for a population parameter based on sample data. C C. To prove the sample statistic is accurate. D D. To calculate the sample mean.

A A. To summarize data B B. To test hypotheses about population means C C. To model the relationship between variables and predict outcomes D D. To measure the spread of data

A A. Binomial distribution B B. Normal distribution C C. Poisson distribution D D. Exponential distribution

A A. Mean = 1, Standard Deviation = 1 B B. Mean = 0, Standard Deviation = 1 C C. Mean = 0, Standard Deviation = 0 D D. Mean = 1, Standard Deviation = 0

A A. No linear relationship between the variables. B B. A perfect positive linear relationship. C C. A perfect negative linear relationship. D D. A strong non-linear relationship.

A A. P(A) + P(B) B B. P(A) * P(B) C C. 0 D D. 1

A A. The probability that the null hypothesis is true. B B. The probability that the alternative hypothesis is true. C C. The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true. D D. The significance level of the test.

A A. The theorem stating that the sample mean always equals the population mean. B B. The theorem stating that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution. C C. The theorem stating that the population must be normally distributed. D D. The theorem describing the center of any dataset.

A A. Binomial distribution B B. Poisson distribution C C. Normal distribution D D. Bernoulli distribution

A A. The total number of data points. B B. The number of independent pieces of information available to estimate a parameter. C C. The level of significance in hypothesis testing. D D. The range of the data.

A A. Causation between two variables B B. The strength and direction of a linear relationship between two variables C C. The difference between means of two groups D D. The variability within a single variable

A A. To prove the null hypothesis is true. B B. To calculate the exact population parameter. C C. To provide evidence for or against the null hypothesis based on sample data. D D. To describe the sample data.

A A. A population is always larger than a sample, but a sample is more accurate. B B. A population is the entire group of individuals we are interested in studying, while a sample is a subset of the population that we actually examine. C C. A sample is used in descriptive statistics, and a population is used in inferential statistics. D D. There is no difference; the terms are interchangeable.

A A. Mean B B. Median C C. Mode D D. Standard Deviation

A A. The error made when calculating the standard deviation of the population. B B. The standard deviation of the sampling distribution of a statistic (like the sample mean). C C. The difference between the sample mean and the population mean. D D. The error due to measurement inaccuracies.

A A. Descriptive statistics describes a sample, while inferential statistics describes a population. B B. Descriptive statistics uses graphs, while inferential statistics uses calculations. C C. Descriptive statistics summarizes data, while inferential statistics makes predictions or generalizations about a larger group based on sample data. D D. Descriptive statistics is more accurate than inferential statistics.