Running head: COURSE PROJECT: NCLEX Memorial Hospital 1
COURSE PROJECT: NCLEX Memorial Hospital 10
Introduction
This project aims to facilitate the improvement of the quality of healthcare services provided to individuals, families and communities at various age levels. Hence, this project used NCLEX Memorial Hospital, where over the past few days there has been a high level of infectious diseases. The dataset collected is from 60 patients whose age range is 35 to 76.
Classification of Variables
The quantitative variable is age. The qualitative variable is infectious diseases. Age is also a continuous variable as it can take on any value. A variable is any quantity that can be measured and whose value varies through the population and here the level of measurement is age, which we shall label a nominal measurement as numbers are used to classify the data.
The Measures of Center and the Measures of Variation
Themeasures of center are some of the most important descriptive statistics one might extrapolate. It helps give us an idea of what the "most" common, normal, or representative answers might be. Essentially, by getting an average, what you are really doing is calculating the "middle" of any group of observations. There are three measures of center that are most often used: Mean, Median and Mode. (NEDARC)
While measures of central tendency are used to estimate "normal" values of a dataset, measures of variation/dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. A proper description of a set of data should include both of these characteristics. There are various methods that can be used to measure the dispersion of a dataset, each with its own set of advantages and disadvantages. (Climate Data Library)
The Measures of Center and the Measures of Variation Calculations
Column1
Mean
61.81667
Standard Error
1.152127
Median
61.5
Mode
69
Standard Deviation
8.924337
Sample Variance
79.64379
Midrange
58.5
Range
41
Conclusion
By looking at the dataset we find that patients after the age of 50 and most likely 60 to be the most affected by infection diseases. Hence, there should be a prevention plan in place to reduce the number of infected or most likely to be affected by various viruses.
Course Project Phase 2
Introduction
The data in the accompanying spreadsheet records the ages of sixty (60) patients at NCLEX Memorial Hospital who, upon admission, were found to be suffering from ...
Running head COURSE PROJECT NCLEX Memorial Hospital .docx
1. Running head: COURSE PROJECT: NCLEX Memorial Hospital
1
COURSE PROJECT: NCLEX Memorial Hospital
10
Introduction
This project aims to facilitate the improvement of the quality of
healthcare services provided to individuals, families and
communities at various age levels. Hence, this project used
NCLEX Memorial Hospital, where over the past few days there
has been a high level of infectious diseases. The dataset
collected is from 60 patients whose age range is 35 to 76.
Classification of Variables
The quantitative variable is age. The qualitative variable is
infectious diseases. Age is also a continuous variable as it can
take on any value. A variable is any quantity that can be
measured and whose value varies through the population and
here the level of measurement is age, which we shall label a
nominal measurement as numbers are used to classify the data.
The Measures of Center and the Measures
of Variation
Themeasures of center are some of the most important
descriptive statistics one might extrapolate. It helps give us an
idea of what the "most" common, normal, or representative
answers might be. Essentially, by getting an average, what you
are really doing is calculating the "middle" of any group of
observations. There are three measures of center that are most
often used: Mean, Median and Mode. (NEDARC)
While measures of central tendency are used to estimate
"normal" values of a dataset, measures of variation/dispersion
are important for describing the spread of the data, or its
variation around a central value. Two distinct samples may have
the same mean or median, but completely different levels of
variability, or vice versa. A proper description of a set of data
2. should include both of these characteristics. There are various
methods that can be used to measure the dispersion of a dataset,
each with its own set of advantages and disadvantages. (Climate
Data Library)
The Measures of Center and the Measures of Variation
Calculations
Column1
Mean
61.81667
Standard Error
1.152127
Median
61.5
Mode
69
Standard Deviation
8.924337
Sample Variance
79.64379
Midrange
58.5
Range
41
Conclusion
By looking at the dataset we find that patients after the age of
50 and most likely 60 to be the most affected by infection
diseases. Hence, there should be a prevention plan in place to
reduce the number of infected or most likely to be affected by
various viruses.
Course Project Phase 2
Introduction
The data in the accompanying spreadsheet records the ages of
sixty (60) patients at NCLEX Memorial Hospital who, upon
3. admission, were found to be suffering from a certain infectious
disease. After the requisite determination of sample mean,
variance, and standard deviation, we then calculate various
confidence intervals by using the Z function (or the affine Q
function). These intervals represent the likelihood that the age
of a patient who is positive for the disease lies within a certain
age range. It also enables us to predict the likely age range of
future admissions who suffer from the indicated disease.
We are asked to find a best point estimate of the population
mean. We are then to construct both a 95% confidence interval
and a 99% confidence interval and, presumably, derive the
attendant parametric descriptions thereof. It is to be assumed
that the underlying data are normally distributed with ÃÆ’ is an
unknown variance.
Calculation of Point Estimate
If we use the variable, N, to represent the number of patients
(that is, sixty) and the random variable, a, to represent the age
of each of the sixty patients, then the mean is determined to be:
E{a} = Σ (ai) / N = 61.8167 while the variance is calculated as:
σ2a = Σ ( ai — E{a} ) = 78.3164 and the standard deviation is
calculated as: σa = (σ2a)½ = 8.8497 which means that the
standard error is determined by: SE = σa / N½ = 1.1425.
The 95% confidence interval is defined as that interval on either
side of the mean that contains 95% of the area of the Gaussian
curve. According to the standard Z tables, the critical value for
95% confidence is 1.96; consequently, one must range 1.96σ on
either side of the mean to encompass 95% of the area. The
corresponding margin of error is 1.96 times SE, or 2.2393.
The interpretation of this 95% confidence interval is that we are
95% confident that patients admitted to NCLEX Memorial
Hospital who suffer from the disease being studied will range in
age from E{a} — 1.96σ to E{a} + 1.96σ. Substituting the
proper values—E{a} = 61.8167 and σa = 8.8497, we find that
E{a} — 1.96σ = 44.4713 and E{a} + 1.96σ = 79.1261. In short,
4. we are 95% confident that such patients will range in age from
44.4713 to 79.1261. Expressed another way, patients who are
admitted to NCLEX Memorial Hospital in the future and are
found positive for the disease are 95% likely to be aged 44.4713
to 79.1261.
The 99% confidence interval is defined as that interval on either
side of the mean that contains 99% of the area of the Gaussian
curve. According to the standard Z tables, the critical value for
99% confidence is 2.576; consequently, one must range 2.576σ
on either side of the mean to encompass 99% of the area. The
corresponding margin of error is 2.576 times SE, or 2.9430.
The interpretation of this 99% confidence interval is that we are
99% confident that patients admitted to NCLEX Memorial
Hospital who suffer from the disease being studied will range in
age from E{a} — 2.576σ to E{a} + 2.576σ. Substituting the
proper values—E{a} = 61.8167 and σa = 8.8497, we find that
E{a} — 2.576σ = 39.0199 and E{a} + 2.576σ = 79.1261. In
short, we are 99% confident that such patients will range in age
from 44.4713 to 84.6135. Expressed another way, patients who
are admitted to NCLEX Memorial Hospital in the future and are
found positive for the disease are 99% likely to be aged 39.0199
to 84.6135.
Comparative Analysis
There are noticeable changes in the interval estimates,
especially in the range according to that of 95% which is the
age group of 44.4713 to 79.1261 whereas the range according to
that of 99% confident is the age group of 39.0199 to 84.6135.
Therefore, A 99% confidence interval is wider than a 95%.
Therefore, it's more likely that it will contain the true value. If I
make a confidence interval narrower with lower variability and
higher sample size it becomes more precise, the likely values
cover a smaller range. If I increase the coverage by using a 99%
calculation it becomes more accurate, the true value is more
likely to be within the range.
5. Course Project Phase 3
The Process of Hypothesis Testing
A hypothesis is a claim (assumption) or statement about a
population parameter such as a proportion, mean, or standard
deviation. However, hypothesis testing is the theory, methods,
and practice of testing a hypothesis by comparing it with the
null hypothesis. The null hypothesis is only rejected if its
probability falls below a predetermined significance level, in
which case the hypothesis being tested is said to have that level
of significance. (Module 3)
It is extremely important to realize that we are not making
definitive conclusions. We are giving probabilistic conclusions.
We are either concluding that the results we get are likely due
to chance, or unlikely.
The 8 Steps of Hypothesis Testing
In researching Hypothesis Testing I have found 5 Step
Hypothesis Testing, 7 Step Hypothesis Testing, 8 Step
Hypothesis Testing, 10 Step Hypothesis Testing and even 12
Step Hypothesis Testing, but for the sake of time and
fulfillment of this assignment we will address the 8 Step
Hypothesis Testing.
Step 1: Express the given claim in symbolic form. Claim: The
mean IQ of statistics students is greater than 110. Step 2: Give
the symbolic form that must be true when the original claim is
false: Symbolic form: μ > 110 Opposite: μ ≤ 110. Step 3:
Identify the null and alternative hypothesis: H0: μ = 110 and
H1: μ > 110. Step 4: Select the Significance Level:(α) is the
probability that the test statistic will fall in the critical region
when the null hypothesis is actually true. Common values are
0.01, 0.05 and 0.10. For this test, use ∝ = 0.05. Step 5: Identify
the Test Statistic and determine its Sampling Distribution: A
test statistic is a value computed from the sample data, used in
making the decision whether or not to reject the null hypothesis.
See the chart below:
6. The test statistic indicates how far our sample deviates from the
assumed population parameter.
Step 6: Find the Value of the Test Statistic, Then Find Either
the P-Value or the Critical Value(s): Using a significance level
of α =0.05, let’s find the critical value for each of these
alternative hypotheses:
P ≠ 0.5: Critical region is in two tails of the normal
distribution. Using the examples from Hypothesis Testing
Explained and Explored, we find the critical values to be z = -
1.96 and z=1.96
P < 0.5: The critical region is in the left tail of the normal
distribution. Hypothesis Testing Explained and Explored, we
find c so P(z < c) = 0.05. The critical value is -1.645
P > 0.5: The critical region is in the left tail of the normal
distribution. Using the examples from Hypothesis Testing
Explained and Explored, we find c so P(z < c) = 0.95. The
critical value is 1.645 .
The P-value is the probability of getting a value of the test
statistic that is at least as extreme as the one obtained for the
sample data. If the P-value is very small (such as less than
0.05), we will reject the null hypothesis. The exact process for
calculating the P-value depends on your alternative hypothesis.
Step 7: Make a Decision: Reject H0 or Fail to Reject H0: Our
final conclusion will always be one of these: Reject the null
hypothesis or Fail to reject the null hypothesis.
7. Step 8: Restate the Decision Using Simple and Nontechnical
Terms: If your original claim contains equality (became H0)
Reject H0: “There is sufficient evidence to warrant rejection of
the claim that…” Fail to Reject H0: “There is not sufficient
evidence to warrant rejection of the claim that…” If your
original claim does not contain equality (was H1) Reject H0:
“The sample data support the claim that…” Fail to Reject H0:
“There is not sufficient sample evidence to support the claim
that…”
Never conclude a hypothesis test with a statement of "reject the
null hypothesis" or "fail to reject the null hypothesis." Always
make sense of the conclusion with a statement that uses simple
nontechnical wording that addresses the original claim. (Module
3)
Critical Value Method versus P-Value Method Analysis
Critical values for a test of hypothesis depend upon a test
statistic, which is specific to the type of test, and the
significance level, α, which defines the sensitivity of the test. A
value of α = 0.05 implies that the null hypothesis is rejected 5
% of the time when it is in fact true. The choice of α is
somewhat arbitrary. (ESH)
Another quantitative measure for reporting the result of a test of
hypothesis is the p-value. The p-value is the probability of the
test statistic being at least as extreme as the one observed given
that the null hypothesis is true. A small p-value is an indication
that the null hypothesis is false. (ESH) My preference is p-value
testing because the p-value method, I think, is more useful in
that by reporting the p-value you allow others to draw their own
conclusions. For example; perhaps you want to test at the 2%
level, but the read wants to test at the 5% level, by reporting the
p-value you can both make conclusions. The fix level, or
critical value, method does not allow for this.
As part 3 of this project has defined parameters we will perform
as instructed.
8. Original Claim
Original Claim: The average age of all patients admitted to the
hospital with infectious diseases is less than 65 years of age.
We shall test the claim using α = 0.05 and assume our data is
normally distributed and σ is unknown.
Null and Alternative Hypothesis
Write the null and alternative hypothesis symbolically and
identify which hypothesis is the claim. The average age of all
patients admitted to the hospital with infectious diseases is less
than 65 years of age and we are testing whether the alternative
is less than (
<
) this value:
65
m
:
H
0
=
Mean age is 65
65
m
:
H
1
<
9. Mean age is less than 65
Sample size
364
=
; sample mean
82
.
61
)
(
=
x
and sample standard deviation
92
.
8
=
s
Left Tailed Test
The null hypothesis must always include the concept of
equality, which means that it must include the logical operators
³
£
=
or
,
,
10. .On the other hand, the alternative hypothesis must always
express the logical opposite of the operators used for the null
hypothesis, which means it should always include
.
or
,
,
<
>
¹
In the abovementioned question, the null hypothesis includes
=
; therefore the alternative hypothesis expresses
<
. Therefore, it is left-tailed hypothesis test because the rejection
region is located to the extreme left of the distribution. A left-
tailed test is conducted when the alternative hypothesis (HA)
contains the condition HA < x (less than a given quantity).
Test Statistic for Hypothesis Test
The general rule of thumb for z-test situations wherein sample
sizes meet the following requirements:
Z-tests require one of two conditions: either the population is
normally distributed with a known variance, or the sample size
is large. However, in the selection at issue, since the sample
11. size is above 30 but the population standard deviation is
unknown, it is t-test that is used.
Test Statistics and P-Value Values
The test statistic converts any sampling distribution into a
standard normal distribution. The solution of the formula gives
the number of standard deviations that a sample mean falls
above or below the population mean stated in the null
hypothesis. This value is compared to the critical value of a
hypothesis test to make a decision. When the obtained value,
i.e. test statistics, exceeds a critical value, we decide to reject
the null hypothesis; otherwise, we retain the null hypothesis. In
the subject case, there is t-statistic:
T-score (obt.)
76
.
2
60
3565
.
0
60
92
.
8
65
82
.
61
-
=
-
=
-
12. =
-
=
n
s
x
m
Where
x
the sample mean and s is the standard deviation of the sample
and
m
is the population mean. The probability of obtaining t-score
(obt.) is stated by the p value. The p-value is a function of the
observed sample results (a test statistic) relative to a statistical
model, which measures how extreme the observation is.
The Critical Value
The t-score that needed to reject Null hypothesis (
)
0
H
is called the critical value for significance. The critical value
depends on the significance level, which we state in the subject
question as α=0.05.
To locate the probability of obtaining a sample mean from a
given population, we use the standard normal distribution. We
will locate the z or t scores in a standard normal distribution
13. that are the cutoffs, or critical values, for sample mean values
with less than a 5% probability of occurrence if the value stated
in the null is true. A critical value is a cutoff value that defines
the boundaries beyond which less than 5% of sample means can
be obtained if the null hypothesis is true. Sample means
obtained beyond a critical value will result in a decision to
reject the null hypothesis. The critical value is
671
.
1
-
=
t
for significance level
05
.
=
a
and df =59 degree of freedom.
Decision
As the sample mean with a t-score less than critical value is
significant at the 0.05 level, Null Hypothesis
)
(
0
H
is rejected. On the basis of the values of critical and t-score
(ob.), the null hypothesis is rejected. The p –value for t-score -
14. 2.76 and 59 degree of freedom is 0.003844, which is less than
0.05. As a result, null hypothesis is rejected.
Final Conclusion
There is sufficient evidence to warrant rejection of the claim
that the average age of all patients admitted to the hospital with
infectious diseases is less than 65 years of age.
References
Climate Data Library. Measures of Dispersion.
http://iridl.ldeo.columbia.edu/dochelp/StatTutorial/Dispersion/i
ndex.html.
Define Hypothesis Testing.
https://www.google.com/?gws_rd=ssl#q=define+hypothesis+test
ing.Engineering Statistics Handbook (ESH) Critical values and
p values.
http://www.itl.nist.gov/div898/handbook/prc/section1/prc131.ht
m.
Module 03 - Hypothesis Testing with One Sample.
https://engage.rasmussen.edu/learn/mod/url/view.php?id=50801
8.
NEDARC. Measures of Center.
http://www.nedarc.org/statisticalHelp/basicStatistics/measuresO
fCenter.html.
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18. Content, Focus, Use of Text/Outside
Sources (50%)
Diagnosis of marketing problem Explanation of the value of
problem definition Formulation of a research problem
Explanation of how interpretting problem
definition stimulates critical thinking
Percent
Possible Points
Analysis and Critical Thinking (30%)
15%
6
15%
6
15%
6
15%
6
60%
24
Analyzes in addition to providing facts
7.5%
3
19. 7.5%
3
7.5%
3
7.5%
3
30%
12
Analysis is well thought out Professional design used to develop
presentation Presentation includes all 7 of the required slides
Title slide and Reference slide
10%
4
100%
20. 40
0
Gross Assignment
Score:
Less: Late Penalty (Per Policy)
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