introductiontoslingdistributions(編輯修改稿)
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【文章內(nèi)容簡(jiǎn)介】 PrenticeHall, Inc. Chap 614 Comparing the Population with its Sampling Distribution 18 19 20 21 22 23 24 0 .1 .2 .3 P(x) x 18 20 22 24 A B C D 0 .1 .2 .3 Population N = 4 P(x) x _ 1 . 5 8σ 21μ xx ??2 . 2 3 6σ 21μ ??Sample Means Distribution n = 2 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 615 If the Population is Normal (THEOREM 61) If a population is normal with mean μ and standard deviation σ, the sampling distribution of is also normally distributed with and xμμ x ?nσσ x ?Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 616 zvalue for Sampling Distribution of x ? Zvalue for the sampling distribution of : where: = sample mean = population mean = population standard deviation n = sample size xμσnσμ)x(z??xBusiness Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 617 Finite Population Correction ? Apply the Finite Population Correction if: ? the sample is large relative to the population (n is greater than 5% of N) and… ? Sampling is without replacement Then 1NnNnσμ)x(z????Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 618 Normal Population Distribution Normal Sampling Distribution (has the same mean) Sampling Distribution Properties ? (. is unbiased ) x xxμμ x ?μxμBusiness Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 619 Sampling Distribution Properties ? For sampling with replacement: As n increases, decreases Larger sample size Smaller sample size x(continued) xσμBusiness Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 620 If the Population is not Normal ? We can apply the Central Limit Theorem: ? Even if the population is not normal, ? …sample means from the population will be approximately normal as long as the sample size is large enough ? …and the sampling distribution will have and μμx ?nσσ x ?Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 621 n↑ Cen
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