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- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/02%3A_Descriptive_StatisticsStatistics naturally divides into two branches, descriptive statistics and inferential statistics. Our main interest is in inferential statistics to try to infer from the data what the population migh...Statistics naturally divides into two branches, descriptive statistics and inferential statistics. Our main interest is in inferential statistics to try to infer from the data what the population might thin or to evaluate the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Nevertheless, the starting point for dealing with a collection of data is to organize, display, and summarize it effectively.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/10%3A_Correlation_and_Regression/10.09%3A_Formula_List\[SS_{xx}=\sum x^2-\frac{1}{n}\left ( \sum x \right )^2\; \; SS_{xy}=\sum xy-\frac{1}{n}\left ( \sum x \right )\left ( \sum y \right )\; \; SS_{yy}=\sum y^2-\frac{1}{n}\left ( \sum y \right )^2 \nonum...SSxx=∑x2−1n(∑x)2SSxy=∑xy−1n(∑x)(∑y)SSyy=∑y2−1n(∑y)2 ˆy=^β1x+^β0where^β1=SSxySSxxand^β0=ˉy−^β1ˉx
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/04%3A_Discrete_Random_VariablesIt is often the case that a number is naturally associated to the outcome of a random experiment: the number of boys in a three-child family, the number of defective light bulbs in a case of 100 bulbs...It is often the case that a number is naturally associated to the outcome of a random experiment: the number of boys in a three-child family, the number of defective light bulbs in a case of 100 bulbs, the length of time until the next customer arrives at the drive-through window at a bank. Such a number varies from trial to trial of the corresponding experiment, and does so in a way that cannot be predicted with certainty; hence, it is called a random variable.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/zz%3A_Back_Matter/20%3A_GlossaryUsing y − y ^ , the actual y-value of a data point minus the y-value that is computed from the equation of the line fitting the data. Of a class of measurements, the number of measurements in the data...Using y − y ^ , the actual y-value of a data point minus the y-value that is computed from the equation of the line fitting the data. Of a class of measurements, the number of measurements in the data set that are in the class. The line that best fits a set of sample data in the sense of minimizing the sum of the squared errors. The probability, if H 0 is true, of obtaining a result as contrary to H 0 and in favor of H a as the result observed in the sample data.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/08%3A_Testing_Hypotheses/8.01%3A_The_Elements_of_Hypothesis_TestingA hypothesis about the value of a population parameter is an assertion about its value. As in the introductory example we will be concerned with testing the truth of two competing hypotheses, only one...A hypothesis about the value of a population parameter is an assertion about its value. As in the introductory example we will be concerned with testing the truth of two competing hypotheses, only one of which can be true.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/zz%3A_Back_Matter
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/09%3A_Two-Sample_Problems/9.02%3A_Comparison_of_Two_Population_Means_-_Small_Independent_SamplesWhen one or the other of the sample sizes is small, as is often the case in practice, the Central Limit Theorem does not apply. We must then impose conditions on the population to give statistical val...When one or the other of the sample sizes is small, as is often the case in practice, the Central Limit Theorem does not apply. We must then impose conditions on the population to give statistical validity to the test procedure. We will assume that both populations from which the samples are taken have a normal probability distribution and that their standard deviations are equal.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/10%3A_Correlation_and_Regression/10.06%3A_The_Coefficient_of_DeterminationThe coefficient of determination estimates the proportion of the variability in the variable y that is explained by the linear relationship between y and the variable x. There are several formulas fo...The coefficient of determination estimates the proportion of the variability in the variable y that is explained by the linear relationship between y and the variable x. There are several formulas for computing. The choice of which one to use can be based on which quantities have already been computed so far.
- https://stats.libretexts.org/Courses/Fresno_City_College/Math_11%3A_Elementary_Statistics/05%3A_Discrete_Random_Variables/5.01%3A_Random_Variables/5.1.01%3A_Probability_Distributions_for_Discrete_Random_VariablesThe probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The proba...The probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P(x) must be between 0 and 1 and the sum of all the probabilities is 1 .
- https://stats.libretexts.org/Courses/Fresno_City_College/Math_11%3A_Elementary_Statistics/07%3A_EstimationIf we wish to estimate the mean μ of a population for which a census is impractical, say the average height of all 18-year-old men in the country, a reasonable strategy is to take a sample, compute it...If we wish to estimate the mean μ of a population for which a census is impractical, say the average height of all 18-year-old men in the country, a reasonable strategy is to take a sample, compute its mean x−, and estimate the unknown number μ by the known number x−. For example, if the average height of 100 randomly selected men aged 18 is 70.6 inches, then we would say that the average height of all 18-year-old men is (at least approximately) 70.6 inches.
- https://stats.libretexts.org/Courses/Fresno_City_College/Math_11%3A_Elementary_Statistics/05%3A_Discrete_Random_Variables/5.02%3A_The_Binomial_DistributionSuppose a random experiment has the following characteristics. There are n identical and independent trials of a common procedure. There are exactly two possible outcomes for each trial, one termed ...Suppose a random experiment has the following characteristics. There are n identical and independent trials of a common procedure. There are exactly two possible outcomes for each trial, one termed “success” and the other “failure.” The probability of success on any one trial is the same number p. Then the discrete random variable X that counts the number of successes in the n trials is the binomial random variable with parameters n and p. We also say that X has a binomial distribution
