The large sample condition can be assumed for simple

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Unformatted text preview: 1 2 4 5 3 A B C E Sample mean 5 1 2 3 5 2.75 1 3 4 5 3.25 ECO 3411 31 Central Limit Theorem • In selecting a random sample of size n from a population, − the sampling distribution of the sample mean x can be approximated by a normal probability distribution as the sample size becomes large − • The sampling distribution of x can be approximated by a normal probability distribution whenever the sample size is large. The large-sample condition can be assumed for simple random samples of size 30 or more • Whenever the population has a normal probability − distribution, the sampling distribution of x has a normal probability distribution for any sample size • Please go to: www.ruf.rice.edu./~lane/rvls.html ECO 3411 32 Sampling Distribution of x • If we use a large (n > 30) simple random sample, the central limit theorem enables us to conclude that the sampling distribution of x can be approximated by a normal probability distribution. • When the simple random sample is small (n < 30), the sampling distribution of x can be considered normal only if we assume the population has a normal probability distribution. ECO 3411 33 Example: UCF • Sampling Distribution of x for the SAT Scores σ 80 σx = = = 14.6 n 30 E ( x ) = µ = 990 ECO 3411 x 34 Example: UCF BUSINESS STUDENTS • Sampling Distribution of x for the SAT Scores What is the probability that a simple random sample of 30 applicants will provide an estimate of the population mean SAT score that is within plus or minus 10 of the actual population mean µ ? In other words, what is the probability that x will be between 980 and 1000? ECO 3411 35 Example: UCF • Sampling Distribution of x for the SAT Scores Sampling distribution of x Area = .2518 Area = .2518 x 980 990 1000 Using the standard normal probability table with z = 10/14.6= .68, we have area = (.2518)(2) = .5036 ECO 3411 36 Relationship Between the Sample Size and the x Sampling Distribution of Suppose we select a simple random sample of 100 applicants instead of the 30 originally considered. E( ) = µ regardless of the...
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This note was uploaded on 01/17/2014 for the course ECO 3411 taught by Professor Staff during the Winter '08 term at University of Central Florida.

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