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Unformatted text preview: Hypothesis Testing So far: H o : = some value assume known Statistical Test: ztest Chapter 9 Inferences Involving One Population Today 1. Confidence Interval for when is NOT known 2. Hypothesis test: = some value when is NOT known 3. Confidence Interval for proportion = p 4. Hypothesis test: Comparing ( p ) to some value 5. Hypothesis test: = some value Why are these all considered 1 population tests? Finally time to consider: NOT known We used the z table when the population standard deviation ( ) is known: If not known, we have to use the sample standard deviation ( s ) to calculate the test statistic t* is the Students tstatistic * = n x z n s x t  = * Question about Known Not Known If Normality cant be assumed, must use a NONPARAMETRIC Test (not covered in this class) t Students t , Students t , Normal distribution Students tdistribution matches normal distribution ( zdistribution) when n is large . When n is smaller  the tdistribution is less peaked and more spread out To test hypotheses, we need to find and critical t values just like for the z distribution Notation: t (df, ) Read as: t of df, t ) df, ( t Onetailed test 2 tailed test 2 2t (df, /2) +t (df, /2) Table 6 deals with both 1 and 2 tailed alternative hypotheses A t value means you are in the left tail but since the tdistribution is symmetric about mean, table only gives + t values What is the 2tailed t value for t (26,0.01) ? Confidence Interval Procedure : Use t in place of z, and use s in place of The formula for the 1  confidence interval for is: 1 df where t (df, /2 29 to = + n n s x n s x t (df, /2 29 Still assumes the sampled population is normally distributed OR that the sample size is large (i.e., SDSM is normally distributed) Sonow we can calculate confidence intervals for using sample data Example: You conduct a study measuring the size of milkweed beetles in Maryland. From your sample data, you calculate a sample mean of 7.8 cm and a sample standard deviation of 2.3 cm based on 17 beetles. Find a 95% confidence interval for the population mean milkweed beetle size. Assume the size of milkweed beetles is normally distributed. Example 3 . 2 and , 8 . 7 , 17 = = = s x n The Sample Evidence : The Statement : Remember: df = n1 1. The tstatistic is used to complete a hypothesis test about a population mean when is not known 2. HypothesisTesting when NOT known 1 df with * = = n n s x t 2. The test statistic: x 3. The calculated t is the number of estimated standard errors is from the hypothesized mean Example: You are interested in the size of the milkweed leaves on which you find your beetles in Western Maryland. For a random sample of 25 leaves you find the mean length is 22.6 cm and the standard deviation was 8.0 cm. Is there any evidence to support the your advisors claim that the average leaf length for beetlecontaining leaves...
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This document was uploaded on 11/04/2011 for the course BIOM 301 at Maryland.
 Fall '08
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