Lecture vid (6)

University of Texas, Rio Grande Valley **We aren't endorsed by this school
PSYC 2301
Aug 8, 2023
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Chapter G standard Error single sample 2 test probability Basics think of it as a histogram sampling Distributions with allvalues within a statistic we A representation of all possiblevalues of a statistic We've already encountered the standard normal distribution Representation of possiblevalves of z with amean of 0 a standard deviation of 1 Creating a sampling Distribution Determine an possiblesamples of size n Calculate the statistic leg mean standard deviation calculate the probability of each valve occurring Proportion of Ave Sampling Distribution of the mean Different samples of size n Yielddifferent samplemeans o X If the samples are at random the mean of the possiblesample means is the population mean we call that discrepancy error more specifically sampling error The sample means have a standarddeviation that is calledthe standard error of the mean or for shortthe standard error a q garstang'd'driation Of 1st test 2 test We canuse the standard error to compute z and its associated probability Ave for z Beyond for samples of size n If weknowthe population mean population standard deviation andhave random sample we can ask what is the probability of finding a samplemean In otherwords we can determine how unusual or extreme a samplemean iswith the specified population parameters and samplesize Oz Oz O Population standard X M 2 x a deviation O 2 test formula 2 score formula Example use z calculator selects 22 stu Pop mean 100 109 100 15 15 2 3 0 I 2 81 meant'd 109 stander 15
Brief Probability Overview probability p the likelihood of an event occurring Range between 0 I O meansthe event cannot occur I means that the event is certain to occur Fair die probability of rolling a 3 is 116 p 1667 Addition Thule To determine the probability of 2 or morepossibilities for a given event add the probabilities Head or tails in a coin pl heads or tails 5 5 1 Probability of a 3 or u in a die pl 3 or 6 1667 t.nu 333 Multiplication Rule Multiply individual probabilities to determine probability of independent events occurringtogether That is two or moreevents occurring together If we toss 2 dice what is the probability of getting too 5 s 1667 1667 027 Additive one event OR Multiplicative oneevent AND another another two ormore events Joint conditionalprobabilities joint probability co occurrence of 2 or more events Conditional probability probability that an event has occurred given another event has occurred joint prob Pl parent seat belt 20 100 30 100 06 cond prob p seatbelt parent 15120 75 we will repeatedly test hypotheses by interpreting the following conditional probability P sample results null
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