DSST Principles Of Statistics Exam Prep

Explanation
Probability theory is the branch of statistics that deals with the analysis of random phenomena. It provides a mathematical framework for quantifying uncertainty and making predictions based on the likelihood of different outcomes. By studying probability theory, statisticians can better understand and analyze the variability and randomness inherent in data. Standard deviation, dispersion, and descriptive statistics are all important concepts in statistics, but they do not specifically focus on the analysis of random phenomena like probability theory does.

Explanation
Dispersion is the part of statistics that focuses on the variation within a distribution. It measures the spread or extent to which data points deviate from the central tendency. It provides information about how the data is distributed and helps in understanding the range, variability, and diversity of the data set. Central tendency, on the other hand, refers to the measure that represents the center or average of the data. Observational study and hypothesis are not directly related to the variation within a distribution.

Explanation
Geometry is not related to statistics because it is a branch of mathematics that deals with the study of shapes, sizes, and properties of figures and spaces. Statistics, on the other hand, is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. While statistics often involves the use of mathematical concepts, it is primarily focused on data analysis and inference, whereas geometry is focused on the properties of shapes and figures.

Explanation
A t-test is a statistical test used to determine if there is a significant difference between the means of two groups. It is not a numerical descriptor of a distribution like the median, mode, or mean, which are measures that summarize the data in a distribution. The median is the middle value in a dataset, the mode is the most frequently occurring value, and the mean is the average value.

Explanation
The given options represent different types of data. Integer is a type of data that represents whole numbers, both positive and negative. Continuous data refers to numerical data that can take any value within a range. Categorical data represents qualitative variables that are divided into categories or groups. Boolean data is a type of data that can take only two values, typically represented as true or false. Therefore, the correct answer is Integer, as it is a type of data.

Explanation
The mode is not an estimator because it is a measure of central tendency that identifies the most frequently occurring value in a dataset. It does not provide any information about the variability or spread of the data, which is the main purpose of an estimator. Variance, mean, and covariance, on the other hand, are all estimators because they provide information about the variability, average, and relationship between variables, respectively.

Explanation
A pivot is a function of random variables that has a known distribution regardless of the parameters. The T value, Chi square statistic, and Z test are all examples of pivots because their distributions are known. However, the F test is not a pivot because its distribution depends on the specific parameters being tested, such as the degrees of freedom. Therefore, the F test is not a pivot random variable.

Explanation
The earliest work in statistics began in 1663. This suggests that statistical analysis and data collection techniques were being developed during this time period. It is important to note that statistics as a field has evolved and progressed significantly since then, but 1663 marks an important milestone in its early development.

Explanation
Isaac Newton was not involved in the development of probability theory. While he made significant contributions to mathematics and physics, his work did not focus on probability theory. Probability theory was primarily developed by Blaise Pascal, Pierre de Fermat, and Gerolamo Cardano. Pascal and Fermat laid the foundation for probability theory with their correspondence on gambling problems, and Cardano made important contributions to the field with his work on games of chance.

Explanation
The method of least squares was first discussed in 1605.