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Unformatted text preview: ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™
STUDENET HANDOUT STATWAY™ STUDENT HANDOUT  7 Lesson 10.1.2 Central Limit Theorem for Sample Means YOU NEED TO KNOW The Central Limit Theorem for Sample Means Given any population with mean µ and standard deviation σ, the sampling distribution of sample means sampled with replacement from random samples of size n will have a distribution that approaches normality with increasing sample size. The mean and standard error of the sampling distribution are: !! = ! !! = !
! . The criteria for the approximate normality of a sampling distribution is that either the population from which we are sampling is normal or the sample size is greater than 30. Very non
normal populations may require samples substantially larger than 30. NEXT STEPS Given a particular sample mean ! from a sample of size !, the standardized value (Z
score) of the sample mean is called the Z
test statistic. This test statistic is computed with the formula !=
!−!
! ! In the previous lesson, we explored acorns from live oak trees. We saw that acorn weights are normally distributed with a mean of 3.75 grams and a standard deviation of 1.02 grams. The population of acorn weights is displayed below. © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™
STUDENET HANDOUT STATWAY™ STUDENT HANDOUT  8 Lesson 10.1.2 Central Limit Theorem for Sample Means
0.25 1.75 3.75 5.75 7.75 Suppose that a sample of 40 acorns is found with a sample mean of 5 grams. The Z
score will help us to better unders...
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 Spring '14

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