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by: Shane Marks


Shane Marks

GPA 3.93

L. Hendrix

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L. Hendrix
Class Notes
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This 4 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 110 at University of South Carolina - Columbia taught by L. Hendrix in Fall. Since its upload, it has received 10 views. For similar materials see /class/229650/stat-110-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.




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Date Created: 10/26/15
472010 Chapter 23 Use and Abuse of Statistical Inference Assumptions The two forms of inference we ve learned are confidence intervals and hypothesis For either of these to be valid we need for the data to come from an unbiased random sample These methods on inference for p require a large enough sample size to approximate the distribution of with a normal distribution Confidence Intervals The confidence level tells us how often the interval catches the true parameter in the long run if we were to take many samples from a opulation and compute a confidence interval rom the resulting data for each one Once ou take your one sample and computea sing e confidence interval it either was one of the correct intervals or one of the incorrect intervalsso it s either ri ht orwrong and so it has probability of 0 or 1 0 containing the true parameter at that point eThis is why we say With 95 confidence instead of With 95 probability 472010 Con dence Intervals For 95 confidence which ofthe following is a true statement a 5 ofthe intervals in the long run contain the true parameter b 95 ofthe intervals in the long run contain the true parameter c We don not know what percentofthe future intervals will contain the parameter Con dence Intervals True or False tis OK to start your quotquot interval interpretation with With 95 probability a TRUE b FALSE Confidence lnte rvals f computed on the same sample a 99 confidence interval will be a Widerthat an 95 interval b Narrowerthan a 95 interval 0 The same width as the 95 interval d Don t know until we compute the intervals 472010 Confidence lnte rvals If we increase the sample size we ll get an interval that is a Wider b Narrower c d The same width as smaller sample size Don t know until we compute the intervals Confidence lnte rvals Confidence intervals are more informative than hypothesis tests because they actually estimate the parameter of interest 39 e and they are easier to Interpret giv confidence intervals whenever possible 95 confidence is a popular confidence level but is not betterthan any other confidence level it is often used out of habit Hypothesis Tests Only finds evidence forthe alternative hypothesis Lack of evidence forthe alternative does not prove the null is true Lack of evidence forthe alternative does not mean the alternative is not truejustthat we didn t find enough evidence to see that it is true 472010 Hypothesis Tests Suppose you conducta hypothesis test and you reject the null hypothesis H and find in favor of the alternative hypothesis lle You can nclude a The null hypothesis is definitely true b The alternative hypothesis is definitely true c The null hypothesis is definitely not true d e The alternative hypothesis is definitely not true Eitherthe null or the alternative hypothesis could Hypothesis Tests Pvalue summarizes evidence for the alternative hypothesis A large sample size makes a test of significance more sensitive reject more often Asmall sample can miss an important difference by being less sensitive reject less often Always report the sample size and your statistic along With your Pva ue The Pvalue determines statisticalsigni cance The Pvalue does NOT determine practical signi cance Hypothesis Tests The a 005 significance level is a very common choice for a significance level it is not a better choicethan any otherlevelit is just Widely used out of habit


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