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# BUSINESS STATISTICS II MGMT 302

Virginia Commonwealth University

GPA 3.98

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This 3 page Class Notes was uploaded by Timmy Eichmann IV on Wednesday October 28, 2015. The Class Notes belongs to MGMT 302 at Virginia Commonwealth University taught by Charles Correia in Fall. Since its upload, it has received 12 views. For similar materials see /class/230686/mgmt-302-virginia-commonwealth-university in Business, management at Virginia Commonwealth University.

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Date Created: 10/28/15

Estimation of Parameters A point estimator is a rule or formula that tells us how to calculate a numerical estimate based on the measurements contained in a sample The single number that results from the calculation is called a point estimate An interval estimator is a formula that tells us how to use sample data to calculate an interval that estimates a population parameter We want to estimate the parameter u We use the sample mean gas our point estimate and we need the distribution of the sample mean to determine the interval Distribution of Sample Mean The expected value E0 u and the standard error SEX 5 n If the sample comes from a normal distribution then the distribution of the sample mean is normal If the sample comes from a nonnormal distribution the distribution of the sample mean approaches a normal distribution as the sample size increases due to the Central Limit Theorem We estimate the parameter u with the confidence interval X 1 Z1 a2 GVn which is in the form of the point estimate d margin of error To estimate a parameter we must have 1 a point estimate 2 the amount of possible error in the point estimate that is an interval thought to contain the parameter value 3 the degree of con dence we can attach to the statement that the parameter value is contained within the interval CI point estimate l margin of error The theoretical interpretation of the con dence coef cient 1 u is we repeatedly collect a sample of size n from the population and construct a lu100 con dence interval for each sample then we expect lu100 of the intervals to contain the true parameter value Ifo is not know then the con dence interval for the mean 1 is X l t1a2n1an Choosing the sample size for estimating a population mean u within a certain margin of error is 2 Il Z 1412 66 We next want to estimate the parameter 1 the population proportion We will use the normal distribution to approximate the binomial distribution for our estimation interval We assume that the sample size is suf ciently large so that that the approximation is valid The condition of suf ciently large will be satis ed if n p 2 5 and n 1p2 5 We need the sample proportion p and the number of successes x in n trials The lu 100 con dence interval for a population proportion 11 is P i Zla2 P139Pn Choosing the sample size for estimating a population proportion 11 within a certain margin of error is n P I39D zzlaZ e2 TEST of HYPOTHESIS We state a claim about the population parameter We take a representative random sample to verify the claim Based on the sample evidence we contradict or support the claim H0uuo Houuo Houuo H1ugtuo H1ultuo H1ugtuo Hltllo The Test Statistic is z E quot0 oNn if G is known or T E quot0 an if G is not known We assume the null hypothesis to be true then determine the probability of getting a sample result like the one given by the test statistic The smaller is this probability the more unlikely that the null hypothesis is true We de ne this probability to be the pvalue Hence the decision is if the pvalue lt a then reject the null hypothesis The conclusion being that the empirical data strongly suggests the alternative hypothesis is true If the pvalue is gt a then do not reject the null hypothesis The conclusion being that the empirical evidence is insufficient to prove the alternative hypothesis is true

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