Đề 3 – Bài tập, đề thi trắc nghiệm online Lý thuyết xác suất và thống kê

A A. Bar chart B B. Pie chart C C. Histogram D D. Scatter plot

A A. Linear Regression B B. Analysis of Variance (ANOVA) C C. Principal Component Analysis (PCA) D D. Chi-Squared Test

A A. A perfect linear relationship between the dependent and independent variables. B B. A high correlation between two or more independent variables. C C. The absence of any correlation between independent variables. D D. The presence of outliers in the data.

A A. The probability of any event is between 0 and 1, inclusive. B B. The probability of the sample space is equal to 1. C C. The probability of the union of disjoint events is the sum of their probabilities. D D. The probability of an event can be a negative number if the event is rare.

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

A A. The standard error of the regression model. B B. The correlation coefficient between the independent and dependent variables. C C. The proportion of variance in the dependent variable that is predictable from the independent variable(s). D D. The p-value for the overall significance of the regression model.

A A. In a large number of trials, the average of the results will approach the expected value. B B. The probability of rare events increases with more trials. C C. The sample mean is always equal to the population mean. D D. Large samples are always more biased than small samples.

A A. A population is a subset of a sample. B B. A sample is a subset of a population. C C. A population is used in statistics, while a sample is used in probability. D D. There is no difference; the terms are interchangeable in statistics.

A A. A subset of the population being studied. B B. The set of all possible outcomes of a random experiment. C C. The average of all possible outcomes. D D. The probability of a specific event occurring.

A A. To ensure every individual in the population has an equal chance of being selected. B B. To reduce bias by randomly selecting participants. C C. To ensure representation from different subgroups within the population. D D. To simplify the data collection process.

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

A A. To increase the size of the training dataset. B B. To evaluate the performance of a model on unseen data and prevent overfitting. C C. To simplify the model by reducing the number of features. D D. To improve the computational efficiency of model training.

A A. The most likely value of the random variable. B B. The average value of the random variable over many trials. C C. The median value of the random variable. D D. The maximum value of the random variable.

A A. Data must be categorical. B B. Data must follow a specific distribution (e.g., normal distribution). C C. Sample sizes must be small. D D. Variables must be independent.

A A. Probability deals with observed data, while statistics predicts future events. B B. Probability reasons from general principles to specific instances, while statistics infers from specific instances to general principles. C C. Probability is used in social sciences, and statistics is used in natural sciences. D D. There is no difference; the terms are interchangeable.

A A. To estimate the exact value of a population parameter. B B. To provide a range of values that is likely to contain the population parameter. C C. To determine if the sample mean is significantly different from zero. D D. To calculate the probability of a Type I error.

A A. Descriptive statistics is used for qualitative data, while inferential statistics is for quantitative data. B B. Descriptive statistics summarizes data, while inferential statistics uses sample data to make generalizations about a population. C C. Descriptive statistics is more complex than inferential statistics. D D. There is no significant difference between them; they are both used for data analysis.

A A. The probability of making a Type I error. B B. The probability of making a Type II error. C C. The probability of correctly rejecting a false null hypothesis. D D. The probability of correctly accepting a true null hypothesis.

A A. To measure the spread of the data. B B. To adjust for the sample size and the number of parameters being estimated, influencing the shape of the test statistic's distribution. C C. To calculate the p-value directly. D D. To determine the level of significance.

A A. Variance B B. Standard deviation C C. Correlation coefficient D D. Expected value

A A. The probability that the null hypothesis is true. B B. The probability of observing data as extreme as, or more extreme than, the data observed, assuming the null hypothesis is true. C C. The probability of rejecting the null hypothesis when it is false. D D. The probability of accepting the null hypothesis when it is true.

A A. The central tendency of a dataset. B B. The number of data points in a dataset. C C. The spread or dispersion of data points around the mean. D D. The median of a dataset.

A A. Standard deviation B B. Variance C C. Median D D. Range

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

A A. Independent events always have the same probability, while dependent events have different probabilities. B B. Independent events occur simultaneously, while dependent events occur sequentially. C C. The outcome of an independent event does not affect the probability of another event, while the outcome of a dependent event does affect the probability of subsequent events. D D. Dependent events are more common in real-world scenarios than independent events.

A A. To increase the sample size of a dataset. B B. To estimate the sampling distribution of a statistic by resampling with replacement from the original sample. C C. To remove outliers from a dataset. D D. To standardize data to have a mean of zero and a standard deviation of one.

A A. The correlation between two different time series. B B. The correlation of a time series with itself at different time lags. C C. The average value of a time series over time. D D. The trend component in a time series.

A A. To calculate the probability of independent events. B B. To update the probability of an event based on new evidence. C C. To determine the sample size needed for a study. D D. To test the goodness of fit of a statistical model.

A A. The sum of independent and identically distributed random variables tends to follow a uniform distribution. B B. The sample mean of a sufficiently large number of independent and identically distributed random variables, regardless of the original distribution's form, will be approximately normally distributed. C C. The variance of a sample is always smaller than the variance of the population. D D. The probability of any event in a sample space is equal.

A A. The height of a student. B B. The temperature of a room. C C. The number of cars passing a point on a highway in an hour. D D. The time it takes to run a marathon.