One-sample Tests of Hypothesis Ka-fu WONG 23 June 2007
... In this extreme example, David obtained the population average mark to check against the statement made by teaching assistant. In this case, rejecting the TA’s statement about the average midterm mark is not a probability statement. However, in a lot of situations, it is impossible to obtain inform ...
... In this extreme example, David obtained the population average mark to check against the statement made by teaching assistant. In this case, rejecting the TA’s statement about the average midterm mark is not a probability statement. However, in a lot of situations, it is impossible to obtain inform ...
Example 5.1 A student prepares for a quiz by studying a list of ten
... i=1 2i = 1. If we define that for any given event A, P(A) is equal to the sum of the probabilities of the simple events in A. Then, P is a probability on Ω. P(A) = 1 − P(Ac) = 1 − P(E1) = 1 − 12 = 12 . Probability of an event A is a number to indicate how big the occurring possibility of event A. So ...
... i=1 2i = 1. If we define that for any given event A, P(A) is equal to the sum of the probabilities of the simple events in A. Then, P is a probability on Ω. P(A) = 1 − P(Ac) = 1 − P(E1) = 1 − 12 = 12 . Probability of an event A is a number to indicate how big the occurring possibility of event A. So ...
Chap4-Probability-F07
... Since we will not cover all of the material included in the book, I recommend you use this handout to guide your reading of sections 4.1 and 4.2 of the book. Read the following notes and the indicated pages of our book. Do the suggested problems. Complete all the problems in this handout. Get help i ...
... Since we will not cover all of the material included in the book, I recommend you use this handout to guide your reading of sections 4.1 and 4.2 of the book. Read the following notes and the indicated pages of our book. Do the suggested problems. Complete all the problems in this handout. Get help i ...
here - Faculty
... “Moe and Larry – they were the best. I enjoyed every minute of it with them. In fact, to show you how wonderful they were, I never liked to be hit with anything. And Larry used to say to me ‘don’t worry Joe, I’ll take it.’ Now that’s the kind of guys they were.” From Stooges: The Men Behind the May ...
... “Moe and Larry – they were the best. I enjoyed every minute of it with them. In fact, to show you how wonderful they were, I never liked to be hit with anything. And Larry used to say to me ‘don’t worry Joe, I’ll take it.’ Now that’s the kind of guys they were.” From Stooges: The Men Behind the May ...
Chapter 5
... Poisson Process • Experiments yielding numerical values of a random variable X, the number of outcomes occurring during a given time interval or in a specified region, are called Poisson experiments. • The given time interval may be of any length, such as a minute, a day, a week, a month, or even a ...
... Poisson Process • Experiments yielding numerical values of a random variable X, the number of outcomes occurring during a given time interval or in a specified region, are called Poisson experiments. • The given time interval may be of any length, such as a minute, a day, a week, a month, or even a ...
Statistics
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.