Đề thi, bài tập trắc nghiệm online Nguyên lý thống kê – Đề 1

An independent samples t-test is specifically designed to compare the means of two unrelated or independent groups. Paired t-tests are for related groups, ANOVA is for more than two groups, and chi-square tests are for categorical data.

Ordinal data has categories with a meaningful order but not necessarily equal intervals between categories. Customer satisfaction ratings fit this description. Temperature in Celsius is interval, colors of cars are nominal, and heights are ratio.

The null hypothesis is a statement of no effect or no difference, which is tested against the alternative hypothesis. Researchers aim to find evidence to reject the null hypothesis in favor of the alternative.

R-squared (coefficient of determination) indicates the goodness of fit of a regression model, specifically the proportion of the variance in the outcome variable that is explained by the predictors. It is not the slope (option 1), correlation (though related to option 2), or p-value (option 4).

A Type I error (false positive) is rejecting a true null hypothesis. A Type II error (false negative) is failing to reject a false null hypothesis. Options 1, 3, and 4 are incorrect descriptions of these errors.

Hypothesis testing is used to evaluate the strength of evidence against a null hypothesis and in favor of an alternative hypothesis. It doesn't 'prove' hypotheses, but rather assesses evidence.

Statistical significance implies that the observed result is unlikely due to random variation if the null hypothesis is true. It doesn't necessarily mean practical importance (option 1), but rather that there's evidence against the null hypothesis. It's the opposite of being due to chance alone (option 2).

Random sampling reduces selection bias and increases the likelihood that the sample accurately reflects the population, which is crucial for valid statistical inference. While it can make data collection more complex, its benefit is in representativeness.

Statistical inference involves using sample data to draw conclusions about the population from which the sample was drawn. Options 1, 2, and 4 describe descriptive statistics or data collection methods, not inference.

The Central Limit Theorem is a cornerstone of statistical inference, stating that the distribution of sample means will be approximately normal for large enough sample sizes, even if the original population is not normally distributed. This is crucial for many statistical tests.

Mean, median, and mode are measures of central tendency, indicating the 'center' of a dataset. Standard deviation is a measure of dispersion or variability.

Bias refers to systematic errors that lead to consistent overestimation or underestimation of the true value, distorting results in a particular direction. It's not random error (option 1) or variability (option 3).

In statistics, a population is the entire set of items or individuals about which we want to draw conclusions. A sample (option 1) is a part of the population.

Descriptive statistics focuses on summarizing and presenting data in a meaningful way, using measures like mean, standard deviation, and graphs. It is not for prediction (option 1), inference (option 2), or causality (option 4).

Statistical power is the probability of correctly rejecting a false null hypothesis (avoiding a Type II error). Higher power is desirable as it increases the chance of detecting a real effect if one exists.

Confidence intervals provide a range of plausible values for a population parameter, along with a confidence level indicating how sure we are that the true parameter lies within that range. They are not single point estimates (option 1) or for hypothesis testing directly (option 3).

Standard deviation specifically measures the dispersion or spread of data points around the mean. Mean, median, and mode are measures of central tendency, not variability.

Stratified sampling aims to ensure representation from different subgroups (strata) within the population. It involves dividing the population into strata and then randomly sampling from each, improving representativeness compared to simple random sampling in some cases. Options 1, 3, and 4 describe other sampling methods.

A sampling distribution is a theoretical distribution of a statistic (like the sample mean) if we were to take many samples from the population and calculate the statistic for each sample. It is fundamental for understanding the behavior of statistics and for statistical inference. Option 1 describes a data distribution, option 3 is population distribution.

Statistical tests are based on certain assumptions about the data (e.g., normality, independence). Violating these assumptions can compromise the validity of the test results and lead to incorrect conclusions. Option 1 and 3 are incorrect about the impact of assumptions, and option 4 is false as different tests have different assumptions.

A histogram is used to visualize the frequency distribution of a single numerical variable, showing the shape and spread of the data. Scatter plots are for two numerical variables, bar charts for categorical data, and pie charts for proportions of a whole.

Nominal data represents categories with no inherent order (e.g., colors, types of cars). Ordinal data is categorical but ordered (e.g., rankings). Interval and ratio data are numerical.

The median is less sensitive to extreme values (outliers) and skewed distributions than the mean. For skewed data or data with outliers, the median often provides a more representative measure of central tendency. The mean is suitable for roughly symmetrical data without significant outliers.

Variance, and its square root standard deviation, quantify the variability or spread of data around the mean. It indicates how far data points are typically from the average value. It is not a measure of central tendency itself (option 1).

Multicollinearity is high correlation among predictor variables in a regression model. It's problematic because it makes it difficult to isolate the unique effect of each predictor and can inflate the variance of coefficient estimates, leading to unreliable results. Options 1, 3, and 4 are incorrect descriptions or implications of multicollinearity.

The p-value is the probability of obtaining the observed results (or more extreme results) if the null hypothesis is actually true. It is not the probability that the null hypothesis is true (option 1).

Ratio scales have a true zero point, meaning zero indicates the absence of the attribute being measured (e.g., height, weight). Interval scales have equal intervals but no true zero point (e.g., temperature in Celsius). Option 1 is the reverse, and option 3 is incorrect about scale types.

Correlation measures the strength and direction of a linear relationship between two variables. It does not imply causation (option 1), and is not about differences in means (option 3) or variability of a single variable (option 4).

Larger sample sizes provide more information about the population, leading to more precise estimates and thus smaller margins of error. Increased sample size reduces uncertainty.

Boxplots (box-and-whisker plots) are designed to display the distribution of a numerical variable, showing key features like the median, quartiles, range, and potential outliers. Option 1 describes contingency tables or mosaic plots, option 2 might involve bar charts or other comparative graphs, and option 4 describes bar charts or pie charts.