TESTS ON A POPULATION PROPORTION in .NET Writer QR Code ISO/IEC18004 in .NET TESTS ON A POPULATION PROPORTION 9-5 TESTS ON A POPULATION PROPORTIONQr-codes barcode library with .netusing visual studio .net todeploy qr barcode with asp.net web,windows applicationAn approximate test based on the normal approximation to the binomial will be given. As noted above, this approximate procedure will be valid as long as p is not extremely close to zero or one, and if the sample size is relatively large. Let X be the number of observations in a random sample of size n that belongs to the class associated with p. Then, if the null hypothesis H0: p p0 is true, we have X N[np0, np0(1 p0)], approximately. To test H0: p p0, calculate the test statistic X np0 1np0 11 p0 2Visual .net qr code iso/iec18004 reader for .netUsing Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications.(9-32)Bar Code barcode library on .netUsing Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.and reject H0: p Visual Studio .NET Crystal barcode printer with .netuse .net crystal barcode generating toinsert bar code in .netp0 if z0 z Control qr-codes size in c# quick response code size with visual c#or z0 QR Code integrating on .netgenerate, create qr code 2d barcode none on .net projectsNote that the standard normal distribution is the reference distribution for this test statistic. Critical regions for the one-sided alternative hypotheses would be constructed in the usual manner. EXAMPLE 9-10 A semiconductor manufacturer produces controllers used in automobile engine applications. The customer requires that the process fallout or fraction defective at a critical manufacturing step not exceed 0.05 and that the manufacturer demonstrate process capability at this level of quality using 0.05. The semiconductor manufacturer takes a random sample of 200 devices and nds that four of them are defective. Can the manufacturer demonstrate process capability for the customer We may solve this problem using the eight-step hypothesis-testing procedure as follows: 1. The parameter of interest is the process fraction defective p. 2. H0: p 0.05 3. H1: p 0.05 This formulation of the problem will allow the manufacturer to make a strong claim about process capability if the null hypothesis H0: p 0.05 is rejected. 4. 0.05 5. The test statistic is (from Equation 9-32) z0 x np0 1np0 11 p0 2Control qr code jis x 0510 data in visual basic.netto compose qr and qr code 2d barcode data, size, image with visual basic.net barcode sdkwhere x 4, n 200, and p0 0.05. 6. Reject H0: p 0.05 if z0 z0.05 1.645 7. Computations: The test statistic is z0 8. 4 20010.052 120010.05210.952 1.95.NET barcode implement for .netusing barcode writer for .net framework control to generate, create barcode image in .net framework applications.1.95 z0.05 1.645, we reject H0 and conclude that the Conclusions: Since z0 process fraction defective p is less than 0.05. The P-value for this value of the test statistic z0 is P 0.0256, which is less than 0.05. We conclude that the process is capable.Code-128c generating with .netusing .net vs 2010 crystal toproduce code 128b in asp.net web,windows applicationCHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE .NET barcode integrated in .netuse .net barcode integrating tomake bar code with .netAnother form of the test statistic Z0 in Equation 9-32 is occasionally encountered. Note that if X is the number of observations in a random sample of size n that belongs to a class of interest, then P X n is the sample proportion that belongs to that class. Now divide both numerator and denominator of Z0 in Equation 9-32 by n, giving Z0 or Z0 X n 1p0 11EAN / UCC - 13 barcode library for .netgenerate, create ean13 none on .net projects P 1p0 11 USPS POSTNET Barcode barcode library on .netusing visual .net crystal todevelop postnet on asp.net web,windows applicationp0 p0 2 n Control qr code image with .netusing .net winforms toproduce qr code jis x 0510 with asp.net web,windows applicationp0 p0 2 n Pdf417 2d Barcode barcode library with c#.netusing barcode integrated for .net vs 2010 control to generate, create pdf-417 2d barcode image in .net vs 2010 applications.(9-33)Control gtin - 12 size with microsoft excelto assign upc symbol and upc-a supplement 5 data, size, image with microsoft excel barcode sdkThis presents the test statistic in terms of the sample proportion instead of the number of items X in the sample that belongs to the class of interest. Statistical software packages usually provide the one sample Z-test for a proportion. The Minitab output for Example 9-10 follows.1D encoder for exceluse excel 1d barcode integrated todraw 1d barcode on excelTest and CI for One Proportion Test of p 0.05 vs p 0.05 Sample X N Sample p 95.0% Upper Bound Z-Value P-Value 1 4 200 0.020000 0.036283 1.95 0.026 * NOTE * The normal approximation may be inaccurate for small samples.Control code-39 size in .net c# barcode 39 size with visual c#.netNotice that both the test statistic (and accompanying P-value) and the 95% one-sided upper con dence bound are displayed. The 95% upper con dence bound is 0.036283, which is less than 0.05. This is consistent with rejection of the null hypothesis Ho: p 0.05.Control ean / ucc - 14 data with .net data for .net9-5.2 Small-Sample Tests on a Proportion (CD Only) 9-5.3 Type II Error and Choice of Sample Size Bar Code encoder on .netusing barcode generator for asp.net website control to generate, create bar code image in asp.net website applications.It is possible to obtain closed-form equations for the approximate -error for the tests in Section 9-5.1. Suppose that p is the true value of the population proportion. The approximate -error for the two-sided alternative H1 : p p0 is a p0 p 1p11 z p0 2 n b a p0 p 1p11 z p0 2 n b (9-34)Control datamatrix image with vbusing barcode integrating for visual .net control to generate, create ecc200 image in visual .net applications.