lesson_10.1.2_version_1.6_student

This test statistic is computed with the formula

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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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