56
PROPORTIONS, ODDS RATIOS AND RELATIVE RISKS
6.4
Difference of two proportions or percentages
Consider the proportions of the hypertensives in the adult male and female populations to be p1 and p2. If x1 males and x2 females respectively were found to b
46
MEANS, STANDARD ERRORS AND CONFIDENCE LIMITS
Example 5.4 Consider the comparisons of the means 1 and 2 of the DBPs of the
two groups in Example 5.3 with samples of sizes n1 , n2 = 15, 10 , means x1 , x2 =
100, 90 , their difference d = 100 90 = 10 and
42
MEANS, STANDARD ERRORS AND CONFIDENCE LIMITS
C V X =S E X =
(5.5)
n
which is devoid of the unit of measurement of X. It expresses the S E X as a
percentage of the mean .
5.3
Estimation of the variance and standard error
From the observations of a ran
80
TESTS OF HYPOTHESES: MEANS AND VARIANCES
From (7.25), u = 33 26 1 0234 = 32 50, which is much larger than
= 5 99. The null hypothesis of the equality of the variances of the weights
of the three groups is rejected at the 5 percent significance level. T
50
MEANS, STANDARD ERRORS AND CONFIDENCE LIMITS
Xi = + i
(5.31)
with E i = 0 and V i = 2 . For the Least Squares (LS) method of estimating ,
n
=
1
2i =
n
Xi
2
(5.32)
1
n
is minimized with respect to . Since d d = 2
n
becomes =
Xi = 0, the estimator for
44
MEANS, STANDARD ERRORS AND CONFIDENCE LIMITS
follows the Students tdistribution with (n 1) degrees of freedom (d.f.). The percentiles of this distribution for the coverage probability of (1 ) are given by
tn 1, 2 and tn 1, 2 . For instance, for the t
88
TESTS OF HYPOTHESES: PROPORTIONS AND PERCENTAGES
x np0 + z
2
np0 q0
(8.15a)
x np0 z
2
np0 q0
(8.15b)
or
With the continuity correction, x in (8.15a) and (8.15b) are replaced by (x 1/2) and
(x + 1 2) respectively. With this correction, the null hypothes
Learning Activity 1  Theme 1
As mentioned last week the planning process begins with an environmental scan of the business and its
relationship to vision and mission statements. Read the following and complete the activities below:
Mohammed Abul and his
Learning Activity 2  Theme 2 & 3
In the planning phase, managers create a detailed action plan aimed at the organizational goals.
Strategic management, or what you will learn as strategizing, is what an organization will do or not do to
achieve the goals
Assignment 1 Role of Manager and Impact of Organizational Theories on Managers
Part 1
Modern Structural Organizational Theory best describes Barts management style when he
first joined Galaxy. There are four basic assumptions of modern structural theory:
Assignment 1 Role of Manager and Impact of Organizational Theories on Managers
Part 2
It is no secret that Management in the 21st century has changed drastically compared to the
management practices by the Industrial Revolution of the 20th century. 21st c
Learning Activity 1  Theme 1&2
One of the longterm goals set out by the LLB owners (from wee k4) is to increase sales in the cowboy
boot line by 15%. The short term goal to accomplish this is to create a sales campaign that targets the
tourist trade. Th
60
PROPORTIONS, ODDS RATIOS AND RELATIVE RISKS
patients screened for admission by a nurse practitioner and 80 percent of the 100
screened by a physiatrist successfully met the functional goals. Find the 95 percent
confidence limits for the (a) percentage
76
TESTS OF HYPOTHESES: MEANS AND VARIANCES
V D = 21 n1 + 22 n2 and S E D = V D . With the difference of the observed
sample means d = x1 x2 , the test statistic for the above null hypothesis becomes
z=
d d0
SE D
(7.17)
For the specified significance leve
96
TESTS OF HYPOTHESES: PROPORTIONS AND PERCENTAGES
estimators p1 , p2 for (p1, p2) are obtained from independent samples of sizes (n1, n2)
for the two treatments and p = n1 p1 + n2 p2 n for the common proportion p from the
combined sample of size n = n1
94
TESTS OF HYPOTHESES: PROPORTIONS AND PERCENTAGES
z z 2 ,
(8.35)
that is, z z 2 or z z 2 , where z is the same as in (8.25) or (8.32). The pvalue of
this test is obtained from 2P Z z .
Example 8.6 As in Example 8.4, consider the increase of HDL for 15
84
TESTS OF HYPOTHESES: PROPORTIONS AND PERCENTAGES
With the continuity correction, x and p in the above expressions and for the
confidence limit are replaced by (x 1/2) and p 1 2n . Since the discrete binomial
variable is approximated by the normal varia
74
TESTS OF HYPOTHESES: MEANS AND VARIANCES
1.2
1
Power
0.8
0.6
0.4
0.2
0
60
80
100
120
140
Mean
Figure 7.4
Power for the test for the mean with the twosided alternative.
1 = 100, 95, 90, 85, 80, 75, 70 , the power for this case becomes the same as in th
72
TESTS OF HYPOTHESES: MEANS AND VARIANCES
Table 7.4 Power for the ttest for the
mean of the HDL with the leftsided
alternative when = 0 05; estimated
variance.
1
Power
40
39
38
37
36
35
35
34
0.050
0.181
0.430
0.711
0.901
0.978
0.978
0.997
x 0 tn 1, s
70
TESTS OF HYPOTHESES: MEANS AND VARIANCES
Equivalently, the null hypothesis is rejected if 0 exceeds the upper confidence limit
Cu = x + z n for .
7.4.1 The pvalue
This probability is obtained from
P X x = 0 = P
X 0 x 0
n n
(7.10)
=P Z z
Example 7.3 F
58
PROPORTIONS, ODDS RATIOS AND RELATIVE RISKS
The S.E.(d) is given by the square root of this estimated variance, and the 1
percent confidence limits for D are obtained from
(6.12)
d z 2 S E d
Example 6.3 Consider the observed numbers x1 = 250, x2 = 150
66
TESTS OF HYPOTHESES: MEANS AND VARIANCES
7.3.1 The pvalue
With the rightsided alternative, the pvalue is the probability of finding the sample
mean as large or larger than the observed mean x when H0 is true. It is obtained from
P X x = 0 = P
X 0 x
68
TESTS OF HYPOTHESES: MEANS AND VARIANCES
where = 0 1 . For a given , as expected, the required sample size increases as
the power increases. For the hypotheses in Example 7.1, if the significance level and
power are considered to be 5 and 90 percent, z
48
MEANS, STANDARD ERRORS AND CONFIDENCE LIMITS
The variance and standard error of D are V D = 2d n and S E D = d n.
Their estimators are given by v D = S2d n and Sd n. When (X, Y) follow the bivariate normal distribution,
tn 1 =
D d
Sd n
(5.25)
follows t
Learning Activity 2  Theme 2
Explain the type of culture that will enhance the organizational alignment of people in LLB;
Explain what organizational culture is and how it relates to the structure of the organization;
Explain why you chose the organizat
Assignment 2: Planning the Future at Galaxy
Part 1
The Product Manager is an important organizational role typically in a technology company. It
is similar in concept to a brand manager at a consumer packaged goods company. The product
manager is often co
International finance
Assignment 1
Question 1
How has electronic system effected trading and market in general?
Answer
Thomson Reuters was first screenbased trading system was launched in 1982 for the interbank market,
where the majority of foreign exch
.MARCH 2002
TOOL KIT
Do You Have a
WellDesigned
Organization?
Creating a new organizational structure
is one ofthe t0ughestand most
politically explosivechallenges
that an executive faces. Here are
nine tests to guide the way.
by Michael Goold and


@
@
O
O
 @
 
@ @
u Markets consist of buyers. These buyers may differ in their wants, resources, locations,
buying attitudes, and buying practices.
u Through market segmentation, companies divide large, heterogeneous markets i
1) Theme 1
Early management theory consisted of numerous attempts at getting to know
these newcomers to industrial life at the end of the nineteenth century and
beginning of the twentieth century in Europe and United States.
Management in the 20th Centur
The Assignment 2
Course: BMGT 364 6983 Management and Organization Theory (2168)
Author Note
Planning the Future at Galaxy
2016
Planning the Future at Galaxy
Introduction
Galaxy Toys is a successful company producing space toys for children of almost all
Most companies have a portfolio of strategic initiatives. It should become the engine that
drives your organization into adaptabilityand it can, with a couple of simple enhancements.
First, every significant source of uncertainty should be addressed with
Management And Organization Theory
Assignment 1 Role of Manager and Impact of Organizational
Theories on Managers
Part 1
Modern Structural Organizational Theory best describes Barts management style when he first
joined Galaxy. There are four basic assump