onsider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if σ1 and σ2 are unknown but we have reason to believe that σ1 = σ2, we can pool the standard deviations. Using sample sizes n1 and n2, the sample test statistic x1 − x2 has a Student's t distribution where t = x1 − x2 s 1 n1 + 1 n2 with degrees of freedom d.f. = n1 + n2 − 2 and where the pooled standard deviation s is s = (n1 − 1)s12 + (n2 − 1)s22 n1 + n2 − 2 Note: With statistical software, select the pooled variance or equal variance options. (a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n1 = 14,x1 ≈ 4.75, and s1 = 2.84 and for region II, n2 = 13, x2 ≈ 3.95, and s2 = 2.41. The two sample standard deviations are sufficiently close that we can assume σ1 = σ2. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) t =

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Description: onsider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if σ1 and σ2 are unknown but we have reason to believe that σ1 = σ2, we can pool the standa

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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onsider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if σ₁ and σ₂ are unknown but we have reason to believe that σ₁ = σ₂, we can pool the standard deviations. Using sample sizes n₁ and n₂, the sample test statistic x₁ − x₂ has a Student's t distribution where

t =

x₁ − x₂

n₁

n₂

with degrees of freedom d.f. = n₁ + n₂ − 2

and where the pooled standard deviation s is

s =

(n₁ − 1)s₁² + (n₂ − 1)s₂²

n₁ + n₂ − 2

Note: With statistical software, select the pooled variance or equal variance options.

(a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n₁ = 14,x₁ ≈ 4.75, and s₁ = 2.84 and for region II, n₂ = 13, x₂ ≈ 3.95, and s₂ = 2.41. The two sample standard deviations are sufficiently close that we can assume σ₁ = σ₂. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.)

t =

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