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# Statistical Methods I STA 2023

University of Central Florida

GPA 3.67

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This 2 page Study Guide was uploaded by Dimitri Torphy on Thursday October 22, 2015. The Study Guide belongs to STA 2023 at University of Central Florida taught by Chung-Ching Wang in Fall. Since its upload, it has received 39 views. For similar materials see /class/227639/sta-2023-university-of-central-florida in Statistics at University of Central Florida.

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Date Created: 10/22/15

mm Descriptive statistics utilizes numerical and graphical methods to look for patterns in a data set to summarize information revealed in a data set and to present that information in a convenient form lnferential statistics utilizes sample data to make estimates decisions predictions and other generalizations about a large set of data Population a set of units that we are interested in studying Sample a subset of the units of a population Census and Sample Measurement is a process we use to assign numerical values to variables of individual population units When we measure a variable for every unit of a population the result is a census of the population If we only measure part of the units in a population the result is a sample of the population Elements of inferential statistics 9K The population or sample of interest 9K One or more variables that are to be investigated 9K Tables graphs or numerical summary tools 9K Identifications of patterns in the data Elements of interferential statistical problems 9K The population of interest 9K One or more variables that are to be investigated 9K The sample of population units 9K The inference about the population based on information contained in the sample 9K A measure of the reliability of the inference Quantitative data measurements that are recorded on a naturally occurring numerical scale Qualitative data measurements that cannot be measured on a natural numerical scale can only be classified into one group Representative sample exhibits characteristics typical of those possessed by the target population Measure of reliability a statement usually quantitative about the degree of uncertainty associated with a statistical inference Chapter 2 BoxPlot distance between points is figured out by 15QR Quantile Quantile Plot the dot chart Stemand Leaf Display all the numbers lying out Mean average Median the middle number when the numbers are in order Mode number that occurs the most Range largest number minus smallest number Standard Deviation s defined as the positive square root of the sample variance s or s V ELM Variance s2 equal to the sum of the squared distances from the mean divided by n1 or s2 217quot 1 Upper Quartile the 75m percentile Lower Quartile the 25m percentile lQR distance between the lower and upper quartile Chebyshev39s Rule Generally at least I 1k2 of the measurements will fall within k standard deviations of the mean for any number ofk greater than 1regardless of the sharp of the frequency distributiona At least 34 of the measurements will fall within the interval x2s x2s for samples and ll20 p20 for populations b At least 89 of the measurements will fall within the interval x3s x3s for samples and ll30 p30 for populations Empirical Rule the empirical rule is a rule of thumb that applies to samples or populations with frequency distributions that are mound shaped a Approximately 68 of the measurements will fall within the interval xs xs for samples and po po for populations b Approximately 95 of the measurements will fall within the interval x2s x2s for samples and ll20 p20 for populations c Approximately 997 of the measurements will fall within the interval x3s x3s for samples and ll30 p30 for populations ZScore suppose x is a measurement from a sample with mean X and standard deviation s The sample Z score of x is 5 Symmetric Skewed one tail of the distribution has more extreme observations than the other tail if the lower part is on left its a right skew and vice versa MoundShaped distribution the mean median and mode are all about the same Chapter 3 Definitions Experiment An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty Sample Point A sample point is the most basic outcomes from an experiment Sample Space Sample space is the collection of all possible sample points from an experiment Event An event is a specific collection of sample points Union The union of two events A and B is the event that either A or B or both occur in a single trail of the experiment We denote the union ofA and B by the symbol A U B Intersection The intersection of A and B is the event that both A and B occur n a single trail of the experiment We denote the intersection of A and B by the symbol A B Complementary Events The complement of an event A is the event that A does not occur This means the complement event of A consists all sample points that are not in event A We denote the complement of event by the symbol AC Mutually Exclusive Events Events A and B are mutually exclusive events if event A and event B have no sample points in common Independent and Dependent Events A and B are independent events if the occurrence of B does not alter the probability that A has occurred That is PAB PA and PBA PB Events A and B are dependent if they are not independent Additive Rule of Probability The probability of the union of events A and B is the sum of probability of event A and the probability of event B minus the probability ofthe intersection of events A and B ie PA U B PA PB PA n B Event A and Event B are mutually exclusive if contains no sample points that is A and B have no sample points in common A and AC has no sample points in common ie A and AC are mutually exclusive Note PA UA PA PA PA nA 0 9K The sum of the probabilities of complementary events equals one that is PA PAC 1 9K Event A and Event AC have no sample points in common 9K Event A and Event AC are mutually exclusive 9K Venn diagram is a good graphical tool for understanding the concept of compound events complementary events and mutually exclusive 9K PA PAC 1 This means the Event A and the Event AC cover the entire sample space The multiplicative rule of probability is used to find the probability of intersection of two events Let A and B be two events the multiplicative rule of probability is PA n B PAB PB PBA PA We say two events A and B are independent events if the probability of the occurrence of one event say A does not alter the probability that another event say B has occurred PAB PA and PBA PB when A and B are independent events If events A and B are independent the multiplicative rule of probability becomes to PA n B PA PB PB PA We say events A and B dependent events def 39 if A and B are not independent 9K Note 1 PA U B PA PB if events A and B are mutually exclusive because PA n B 0 2 PA n B PA PB if events A and B are independent events The Multiplicative Rule you are drawing one element from each ofk sets of elements with size ni n2 nk respectively The number of different sample points of this experiment is equal to the product anannk Permutations Rule You are drawing n elements from a set of N elements and arranging these n elements in a distinct order The number of different outcomes of this experiment is equal to N Nn 9K Note 1N NN1N2 21 2554321 120 Combinations Rule you are drawing n elements from a set of N elements The number of different outcomes of this experiment is equal to N Nn nl Since the order is of important Partitions Rule pg160 You are partitioning a set on N elements into K groups consisting of elements Nni n2nkThe number l of different outcomes of this experiment is y 39 n1gtltn2lgtltnkl

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