INFERENCE ON TWO POPULATION PROPORTIONS in .NET

Connect Denso QR Bar Code in .NET INFERENCE ON TWO POPULATION PROPORTIONS
INFERENCE ON TWO POPULATION PROPORTIONS
Assign qr code in .net
using barcode implement for visual .net control to generate, create qrcode image in visual .net applications.
We now consider the case where there are two binomial parameters of interest, say, p1 and p2, and we wish to draw inferences about these proportions. We will present large-sample hypothesis testing and con dence interval procedures based on the normal approximation to the binomial.
QR Code barcode library with .net
Using Barcode decoder for .NET Control to read, scan read, scan image in .NET applications.
10-6.1
.net Framework barcode integrated on .net
using .net framework toembed bar code on asp.net web,windows application
Large-Sample Test for H0: p1
decode bar code on .net
Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Suppose that two independent random samples of sizes n1 and n2 are taken from two populations, and let X1 and X2 represent the number of observations that belong to the class of interest in samples 1 and 2, respectively. Furthermore, suppose that the normal approximation to the binomial is applied to each population, so the estimators of the population proportions
Control qr-code data with c#
qr code 2d barcode data in c#
CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES
Control denso qr bar code image on .net
using barcode encoding for web control to generate, create qr code iso/iec18004 image in web applications.
P1 X1 n1 and P2 X2 n2 have approximate normal distributions. We are interested in testing the hypotheses
Control qr code iso/iec18004 image on vb.net
use .net quick response code development toreceive qr codes on vb
H0: p1 H1: p1 The statistic B
Barcode drawer on .net
use .net framework crystal barcode printing toassign bar code in .net
p2 p2
Bar Code barcode library for .net
using barcode drawer for visual .net control to generate, create bar code image in visual .net applications.
p1 11
Connect linear 1d barcode with .net
use .net framework 1d barcode implementation tomake linear barcode in .net
P1
Quick Response Code barcode library with .net
use .net framework crystal quick response code drawer toconnect qr-codes for .net
P2
Identcode printing in .net
using .net crystal touse identcode on asp.net web,windows application
p1 2
Control pdf417 data in .net
pdf417 2d barcode data on .net
1 p1
Code 39 barcode library for .net
using sql 2008 togenerate code 39 on asp.net web,windows application
p2 11
Control ean / ucc - 13 image on vb.net
use visual studio .net european article number 13 printing tointegrate ean / ucc - 13 with vb.net
p2 2 n2
Control ucc - 12 data on .net
to include upc-a and upca data, size, image with .net barcode sdk
p2 2
Control code39 image in .net
using asp.net website toreceive code 39 extended with asp.net web,windows application
(10-32)
Ean 128 Barcode development for visual basic
use .net winforms crystal ean 128 integrated torender ean 128 on visual basic
is distributed approximately as standard normal and is the basis of a test for H0: p1 p2. Speci cally, if the null hypothesis H0: p1 p2 is true, using the fact that p1 p2 p, the random variable Z B
Control upc a image on excel spreadsheets
generate, create upca none with excel projects
P1 P2
Control code 3 of 9 data for excel
to develop bar code 39 and code39 data, size, image with excel barcode sdk
1 p2 a n
1 n2 b
is distributed approximately N(0, 1). An estimator of the common parameter p is
X1 n1
X2 n2
The test statistic for H0: p1
p2 is then Z0
P1 P 11
P2
1 P2 a n
1 n2 b
This leads to the test procedures described below.
Null hypothesis: Test statistic:
H0: p1 Z0
P1 P 11 P2 1 P2 a
1 n2 b Rejection Criterion z0 z0 z0 z z
2 or z0
(10-33)
Alternative Hypotheses H1: p1 H1: p1 H1: p1 p2 p2 p2
10-6 INFERENCE ON TWO POPULATION PROPORTIONS
EXAMPLE 10-14
Extracts of St. John s Wort are widely used to treat depression. An article in the April 18, 2001 issue of the Journal of the American Medical Association ( Effectiveness of St. John s Wort on Major Depression: A Randomized Controlled Trial ) compared the ef cacy of a standard extract of St. John s Wort with a placebo in 200 outpatients diagnosed with major depression. Patients were randomly assigned to two groups; one group received the St. John s Wort, and the other received the placebo. After eight weeks, 19 of the placebo-treated patients showed improvement, whereas 27 of those treated with St. John s Wort improved. Is there any reason to believe that St. John s Wort is effective in treating major depression Use 0.05. The eight-step hypothesis testing procedure leads to the following results: The parameters of interest are p1 and p2, the proportion of patients who improve following treatment with St. John s Wort ( p1) or the placebo ( p2). 2. H0: p1 p2 3. H1: p1 p2 4. 0.05 5. The test statistic is 1. z0 B
p1 p 11 p2
1 p2 a n 19 100 19 100
1 n2 b 0.19, n1 n2 100, and
where p1
27 100
0.27, p2
x1 n1
x2 n2
27 100
0.23 z0.025 1.96.
6. 7.
p2 if z0 z0.025 1.96 or if z0 Computations: The value of the test statistic is z0 1 0.2310.772 a 100 B 0.27 0.19 1 b 100
Reject H0: p1
Conclusions: Since z0 1.35 does not exceed z0.025, we cannot reject the null hypothesis. Note that the P-value is P 0.177. There is insuf cient evidence to support the claim that St. John s Wort is effective in treating major depression.
The following box shows the Minitab two-sample hypothesis test and CI procedure for proportions. Notice that the 95% CI on p1 p2 includes zero. The equation for constructing the CI will be given in Section 10-6.4. Test and CI for Two Proportions Sample X N Sample p 1 27 100 0.270000 2 19 100 0.190000 Estimate for p(1) p(2): 0.08 95% CI for p(1) p(2): ( 0.0361186, 0.196119) Test for p(1) p(2) 0 (vs not 0): Z 1.35 P-Value 0.177
364 10-6.2 10-6.3
CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES
Small-Sample Test for H0: p1
p2 (CD Only)
-Error and Choice of Sample Size
The computation of the -error for the large-sample test of H0: p1 p2 is somewhat more involved than in the single-sample case. The problem is that the denominator of the test statistic Z0 is an estimate of the standard deviation of P1 P2 under the assumption that p1 p2 p. When H0: p1 p2 is false, the standard deviation of P1 P2 is B p1 11 p1 2 p2 11 p2 2