CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN in .NET

Creation QR Code in .NET CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
8-2 CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
Encode qr with .net
generate, create qr code none on .net projects
Con dence and tolerance intervals bound unknown elements of a distribution. In this chapter you will learn to appreciate the value of these intervals. A prediction interval provides bounds on one (or more) future observations from the population. For example, a prediction interval could be used to bound a single, new measurement of viscosity another useful interval. With a large sample size, the prediction interval for normally distributed data tends to the tolerance interval in Equation 8-1, but for more modest sample sizes the prediction and tolerance intervals are different. Keep the purpose of the three types of interval estimates clear: A con dence interval bounds population or distribution parameters (such as the mean viscosity). A tolerance interval bounds a selected proportion of a distribution. A prediction interval bounds future observations from the population or distribution.
Visual Studio .NET qr-codes recognizer in .net
Using Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.
8-2 CONFIDENCE INTERVAL ON THE MEAN OF A NORMAL DISTRIBUTION, VARIANCE KNOWN
Barcode creator in .net
generate, create bar code none for .net projects
The basic ideas of a con dence interval (CI) are most easily understood by initially considering a simple situation. Suppose that we have a normal population with unknown mean and known variance 2. This is a somewhat unrealistic scenario because typically we know the distribution mean before we know the variance. However, in subsequent sections we will present con dence intervals for more general situations.
Get bar code with .net
generate, create barcode none on .net projects
8-2.1
Control qr code jis x 0510 data for visual c#
to generate qr and qr code 2d barcode data, size, image with visual c#.net barcode sdk
Development of the Con dence Interval and its Basic Properties
QR Code generator with .net
using barcode implementation for asp.net webform control to generate, create qr-code image in asp.net webform applications.
Suppose that X1, X2, p , Xn is a random sample from a normal distribution with unknown mean and known variance 2. From the results of 5 we know that the sample mean X is normally distributed with mean and variance 2 n. We may standardize X by subtracting the mean and dividing by the standard deviation, which results in the variable Z X 1n (8-3)
Control qr bidimensional barcode image for visual basic.net
using barcode encoding for .net vs 2010 control to generate, create quick response code image in .net vs 2010 applications.
Now Z has a standard normal distribution. A con dence interval estimate for is an interval of the form l u, where the endpoints l and u are computed from the sample data. Because different samples will produce different values of l and u, these end-points are values of random variables L and U, respectively. Suppose that we can determine values of L and U such that the following probability statement is true: P 5L U6 1 (8-4)
Barcode 3 Of 9 writer on .net
using visual .net tocompose code 39 full ascii on asp.net web,windows application
where 0 1. There is a probability of 1 of selecting a sample for which the CI will contain the true value of . Once we have selected the sample, so that X1 x1, X2 x2, p , Xn xn, and computed l and u, the resulting con dence interval for is l u (8-5)
Linear barcode library for .net
use .net linear barcode generating torender linear barcode in .net
CHAPTER 8 STATISTICAL INTERVALS FOR A SINGLE SAMPLE
Barcode barcode library in .net
use vs .net crystal bar code encoder toencode bar code for .net
The end-points or bounds l and u are called the lower- and upper-con dence limits, respectively, and 1 is called the con dence coef cient. 2 1 1n2 has a standard normal distribuIn our problem situation, because Z 1X tion, we may write Pe z X
2d Matrix Barcode barcode library with .net
generate, create matrix barcode none with .net projects
1 1n
.net Framework Crystal leitcode integration with .net
generate, create leitcode none on .net projects
Now manipulate the quantities inside the brackets by (1) multiplying through by subtracting X from each term, and (3) multiplying through by 1. This results in P eX z 1n X z f 1
Incoporate barcode on java
using ireport touse barcode in asp.net web,windows application
1n, (2)
Code 3 Of 9 printer in office excel
use office excel barcode 39 development toincoporate code39 on office excel
(8-6)
Visual Studio .NET 3 of 9 barcode decoder on .net
Using Barcode scanner for visual .net Control to read, scan read, scan image in visual .net applications.
From consideration of Equation 8-4, the lower and upper limits of the inequalities in Equation 8-6 are the lower- and upper-con dence limits L and U, respectively. This leads to the following de nition. De nition 1n 1n
Pdf417 2d Barcode implementation in vb.net
using .net vs 2010 todevelop barcode pdf417 for asp.net web,windows application
If x is the sample mean of a random sample of size n from a normal population with known variance 2, a 100(1 )% CI on is given by x where z
Control upc a data with vb.net
to use upca and universal product code version a data, size, image with visual basic barcode sdk
(8-7)
Generate gs1 - 13 with .net
using barcode maker for asp.net web control to generate, create european article number 13 image in asp.net web applications.
is the upper 100
Control uss-128 size on .net
to receive gs1 barcode and ucc.ean - 128 data, size, image with .net barcode sdk
2 percentage point of the standard normal distribution.
ANSI/AIM Code 128 development on .net
generate, create code128b none on .net projects
EXAMPLE 8-1
ASTM Standard E23 de nes standard test methods for notched bar impact testing of metallic materials. The Charpy V-notch (CVN) technique measures impact energy and is often used to determine whether or not a material experiences a ductile-to-brittle transition with decreasing temperature. Ten measurements of impact energy (J) on specimens of A238 steel cut at 60 C are as follows: 64.1, 64.7, 64.5, 64.6, 64.5, 64.3, 64.6, 64.8, 64.2, and 64.3. Assume that impact energy is normally distributed with 1J. We want to nd a 95% CI for , the mean 10, 1, and impact energy. The required quantities are z 2 z0.025 1.96, n x 64.46. The resulting 95% CI is found from Equation 8-7 as follows: x 64.46 1n 1 1.96 110 63.84 z
64.46 65.08
1 110
That is, based on the sample data, a range of highly plausible vaules for mean impact energy for A238 steel at 60 C is 63.84J 65.08J. Interpreting a Con dence Interval How does one interpret a con dence interval In the impact energy estimation problem in Example 8-1 the 95% CI is 63.84 65.08, so it is tempting to conclude that is within