STA3032 Module 3.1-3.1.2
STA3032 Module 3.1-3.1.2 STA3032
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This 2 page Class Notes was uploaded by Tia Belvin on Thursday February 18, 2016. The Class Notes belongs to STA3032 at University of Florida taught by Demetris Athienitis in Spring 2016. Since its upload, it has received 268 views. For similar materials see Engineering Statistics in Engineering and Tech at University of Florida.
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Date Created: 02/18/16
STA3032 MODULE 3 ARTICLE I. 3.1 INFERENCE FOR ONE POPULATION 1) When a population parameter is estimated by a sample statistic, this sample estimate is not 100% representative of the population because it varies from sample to sample. 3.1.1 CONFIDENCE INTERVALS 1) Confidence Interval (CI): reports an interval of plausible values based on the point estimate sample statistic and its standard deviation a. To calculate a confidence interval you first i. Select the confidence level 100(1-α)% ii. If the sample is replicated many times, the proportion of times that the CI will not contain the population parameter is α 2) Known population variance a. Assume you have µ and σ 2 i. The methodology to calculate a CI will require a normal distribution such that ▯▯ X ~ N(μ, ▯ ) for ▯ > 30 ii. If n is less than 30 then we will use t values instead of Z *will be elaborated on later in notes* iii. Note that b. If the data is normally distributed, you calculate CI using Z scores i. The probability that the CI interval- -contains the true value of µ is 1-α. ii. In most cases CI will be constructed from a singlesample and we can no longer talk about probability 1. But we can say that we are 100(1-α)% confident that the methodology by which the interval was contrived will contain the true population parameter (most of the time µ) 3) Unknown population variance 2 2 a. When a sample size is large we can assume that s is representative of σ b. When you don’t know the population variance (σ ), you use the t-test i. The t-test is determining the confidence interval using a t value instead of z STA3032 ii. Note that *where t= t n-1 iii. The n-1 is for degrees of freedom (v=n-1) which isused when finding the necessary value on the t-table 3.1.2 HYPOTHESIS TESTS 1) A statistical hypothesis is the claim that some population characteristic is equal to a certain value a. The null hypothesis (denoted by H ) i0 the hypothesis that is initially assumed to be true b. The alternate hypothesis (denoted by H ) is1the complementary to H , usua0ly the hypothesis that is wished to be tested. 2) Test procedure a. Created under the assumption of the null and then it is determined how likely that assumption is compared to the alternate i. Test statistic- a function of the sampled data ii. Rejection region/criteria- set of all test statistic values for which the null will be rejected b. Error types i. Type I error consists of rejecting the null when itis in fact true ii. Type II error consists of failing to reject the null when it is in fact false
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