ABSTRACT
A simple point estimate https://www.w3.org/1998/Math/MathML"> θ ˆ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2157.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> of a parameter https://www.w3.org/1998/Math/MathML"> θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2158.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> serves as a best guess for the value of https://www.w3.org/1998/Math/MathML"> θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2159.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , but conveys no sense of confidence in the estimate. A confidence interval I, based on https://www.w3.org/1998/Math/MathML"> θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2160.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , is used to make statements about https://www.w3.org/1998/Math/MathML"> θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2161.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> when the sample size, the underlying distribution of https://www.w3.org/1998/Math/MathML"> θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2162.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , and the confidence coefficient https://www.w3.org/1998/Math/MathML"> 1 - α https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429181467/18b385cc-0cd0-46cd-861b-2292640d7e62/content/eq2163.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> are known. We make statements of the form:
