Measures of variation, confidence intervals, and population means

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Module 01 Course Project
1
Course Project Phase 01
Rachel Nolasco
Rasmussen College
Author Note
This paper is being submitted on January 6, 2018 for Russell Frith?s STA3215 Section 01
Inferential Statistics and Analytics – Online Plus – 2018 Winter Quarter
Module 01 Course Project
2
Course Project Phase 01
There has been a noticeable increase in numbers of patients with a particular type of
infectious diseases admitted into NCLEX Memorial Hospital in the Infectious Diseases Unit
within the past few days. In order to treat patients in the correct fashion a statistical analysis must
be conducted to gather information. The information collected will include:
?
Client Number
?
Infectious Disease Status
?
Age of Patient
The set of data collected includes 60 patients that range from the ages of 35 to 76 which have all
been admitted to the infectious disease unit.
The quantitative data represented for this study includes the ages of the patients that have
been admitted with the disease in question. The client numbers that represent each patient are
considered discreet variables and can be used to count and keep track of patients and their
information. There are four levels of measurement that could possibly be applied to a variable:
nominal, ordinal, interval, and ratio. The client number is considered interval. The difference
between one numbers to the next is always the same. The disease status of each patient is
considered nominal. Each patient either has the disease or does not. The age of the patient is the
ratio. This is because the distance between ages can be measured.
Module 01 Course Project
3
Identifying a single value that can describe a large set of data is sometimes difficult. The
central tendency of is a range of numbers that can best describe the set of data. The central
tendency is decided by the mean (average), median (middle), or mode (most common)
item/number that appears in the data set. The range of data, or the difference between the
smallest and largest number, can be represented by the central tendency more accurately when
the range of data is small versus when the range of data is large.
The set of data from the statistical analysis of NCLES Memorial Hospital?s Infectious
Disease Unit shows that sixty individuals from the ages of 35 to 76 were admitted to the hospital
with a specific disease within the last few days. The statistical analysis being performed is meant
to provide information on the ages of the infected patients and how that information can be used
to treat the disease. The mean or average age of patients being admitted is 61.8 years old. The
median age is 62.5 years. While the mode or most frequently admitted age is 69. It is important
to be able to track these numbers because the data has the ability to give professionals a more
clear idea of the group of people who are currently infected as well as those who are likely to
become infected in the future.
This information presented by the statistical analysis is also important to decide which
treatments are best and most likely able to cure the patients. Statistical data is used to collect,
analyze, and infer information about a specific topic. This information is often used to evaluate
creditability and aid in decision making. By collecting data in a statistical analysis the
information can be easily shared and credited by those who may be in need of it.
Module 01 Course Project
4
References
The Role of Statistics in Research. (n.d.). Retrieved January 6, 2018, from
https://www.bcps.org/offices/lis/researchcourse/statistics_role.html
Rouse, M. (2014, October). statistical mean, median, mode and range. Retrieved
January 6, 2018, from http://searchdatacenter.techtarget.com/definition/
statistical-mean-median-mode-and-range
Running head: Module 02 Course Project
1
Course Project – Phase 02
Rachel Nolasco
Rasmussen College
Author Note
This paper is being submitted on January 13, 2018, for Russell Frith?s STA3215 Section 01
Inferential Statistics and Analytics – Online Plus – 2018 Winter Quarter
Course Project – Phase 02
Module 02 Course Project
2
NCLEX Memorial Hospital is currently experiencing an increase in the number of
patients suffering from infectious disease. I believe that age of the patient plays a crucial role
in the development of infectious disease. This is based on the fact that increase in age causes
immune system to become weak, making individuals being more susceptible to infectious
disease. In order to test the claim, data on sixty patients were collected from MCLEX
Memorial Hospital.The data included information about the age of the patients, client number
and infectious disease status. These patients belonged to NCLEX hospital with age ranging
from 35 years to 76 years of age.The objective is to find the best point estimate of the
population along with calculating the confidence interval of the given age range.
Confidence interval in simple term can be said to be a type of interval estimate which
is computed from the given data (“7.1.4. What are confidence intervals??, n.d.). It is seen that
a random sample of the population is taken for the study, and statistics such as mean is
calculated from the data, to approximate the mean of the population.It is necessary for the
sample statistics to fit into the underlying population parameter. There always is an issue of
fitting the sample statistics to estimate the population parameter. Since the confidence
interval contains a range of values for the sample statistics, therefore it helps in solving this
issue.
Population parameter is generally estimated by a single estimate which is nothing but
a point estimate. A sample mean x is a point estimate of the population mean µ.A confidence
interval is generally calculation from the sample estimate to generalize for the whole
population. According to Altman (2005),?The CI is a range of values either side of the
estimate between which we can be 95% sure that the true value lies. ?Confidence intervals
are needed because they are useful for avoiding misinterpretation of the non-significant result
of small studies (Altman, 2005).
Module 02 Course Project
3
Confidence Interval of NCLEX Memorial Hospital Patient?s data
A descriptive statistics of the patient?s shows that the mean age of the patient is 61.82
year.
95% Confidence interval
Since the data is assumed to be normally distributed and population standard
deviation is not known, therefore a t-test will be used to construct the confidence interval.
Sample mean,x-bar = 61.82
Sample standard deviation,s=8.924
Sample size, n=60
Standard error of the sample,se = s/sqrt(n) =8.924/sqrt(60) = 1.152
Critical t-value = 2.001 with 59 degree of freedom calculated using Excel function
=T.INV.2T(0.05,59)
Margin of error,e = Standard error*Critical t-value =1.152*2.001 = 2.305
Lower Limit =x-bar-e =61.82-2.305 = 59.51
Upper limit =x-bar = 61.82.305 = 64.12
99% Confidence interval
Sample mean,x-bar = 61.82
Sample standard deviation,s=8.924
Sample size ,n=60
Standard error of the sample,se = s/sqrt(n) =8.924/sqrt(60) = 1.152
Critical t-value = 2.662 with 59 degree of freedom calculated using Excel function
=T.INV.2T(0.01,59)
Margin of error,e = Standard error*Critical t-value =1.152*2.662 = 3.067
Lower Limit =x-bar-e =61.82-3.067 = 58.75
Upper limit =x-bar = 61.82.067 = 64.88
Module 02 Course Project
4
Confidence interval Interpretation
`95% confidence Interval:We are 95% confident that the mean age of patients
admitted in MCLX hospital because of infectious disease is between 59.51 year and 64.12
year.Also,if repeated samples of the patient?s age is taken and 95% confidence interval is
calculated for each sample then 95% of the interval would contain the population mean.
99% Confidence Interval: We are 99% confident that the mean age of patients
admitted in MCLX hospital because of infectious disease is between 58.75 year and 64.88
year. Also,if repeated samples of the patient?s age is taken and 99% confidence interval is
calculated for each sample then 95% of the interval would contain the population mean.
Comparison
A comparison of the 99% and 95% confidence interval shows that the 99%
confidence interval is wider compared to 95% confidence interval. In other word, the spread
in calculating CI of patient?s age is more compared to 95% confidence interval. The
difference arises because the critical t-value of 99% CI is more compared to 95% CI causing
a greater value of margin of error.
Conclusion
From the above calculation of CI of patient?s age, it becomes clear that a 99%
confidence interval is wider compared to 95% confidence interval. In general, it can be
concluded that increasing the confidence interval increases the width of the interval because
of increase in standard error of the sample while keeping sample size as constant.
Module 02 Course Project
5
References
7.1.4. What are confidence intervals?. Itl.nist.gov. Retrieved 13 January 2018, from
http://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm
Altman, D. (2005). Why We Need Confidence Intervals. World Journal Of Surgery, 29(5),
554-556. http://dx.doi.org/10.1007/s00268-005-7911-0
Lane, D. (N.d.). Confidence Intervals Introduction. Onlinestatbook.com. Retrieved 13
January 2018, from http://onlinestatbook.com/2/estimation/confidence.html
1
Course Project – Phase 03
Rachel Nolasco
Rasmussen College
Author Note
This paper is being submitted on January 21, 2018, for Russell Frith?s STA3215 Section 01
Inferential Statistics and Analytics – Online Plus – 2018 Winter Quarter
Hypothesis Testing Process
HYPOTHESIS TESTING
2
Hypothesis testing has widely gained popularity among researchers, where a claim
about the population parameter is tested. Based on the result obtained from the sample data,
inference about the population is made. There exists a different type of hypothesis test which
depends on the nature of the data. There are eight steps in hypothesis testing which are
described below.
Step 1: Stating the null (Ho) and alternative hypothesis (Ha)
It is the first step in performing hypothesis test of the sample. There are two types of
claim, one related to the claim about the population and other different from the claim. The
null and alternative hypothesis is stated in a mutually exclusive manner. A null hypothesis
will always contain an equal to sign. It would say that the population parameter is equal to a
hypothesized value. Based on some previous knowledge an initial claim is made. However,
an alternative hypothesis is just the opposite of null hypothesis, where a population parameter
is assumed as smaller, greater or different than the hypothesized value as stated in the null
hypothesis.
Step 2: Choose the level of significance(alpha)
A significance level is denoted by alpha (a).According to Downing and Clark
(2010),?Significance level is the probability of rejecting the null when it is true.? A
significance level of 0.0.1 indicates there is a 1% chance of concluding that a difference
exists when the reality is there is no actual difference. Choosing the level of significance of
the hypothesis is essential. Generally, a significance level of 0.05 is selected for most of the
hypothesis testing process. A p-value calculated in the hypothesis test is then compared with
the chosen significance level which is then used to determine whether to accept or reject the
null.
HYPOTHESIS TESTING
3
Step 3: Determine the appropriate test statistic to use
After choosing the significance level, a proper test to be performed is determined.For
example, when the population standard deviation is known,z-test is used.Also, in case of
unknown standard deviation of the population, the t-test is used to test the hypothesis.The
calculation of appropriate test statistic help in comparing with what is expected under the null
hypothesis. Based on comparison with the critical value of the given test statistic, it is
decided whether to reject the null or not. This approach is called as critical value approach.
Step 4: Value of the test-statistic
After determining the type of test statistic to be used, data is collected for the sample.
Based on the sample data t-statistic is calculated, which is again used to calculate the p-value.
Step 5: Compute the p-value from the test statistics
Based on the calculation of test statistic from sample data, the p-value is calculated.A
p-value is compared with the chosen significance level, and the decision is made regarding
the claim. If the p-value is less than the significance level (alpha), then the null hypothesis is
rejected, else, it is accepted.
Step 6: Determine the critical value
It is an important step in hypothesis testing where the critical value is calculated based
on the chosen significance level. The obtained critical value is then compared with the test
statistic where a decision regarding whether to accept or reject the null is made.
Step 7: Make the statistical decision
The statistical decision of whether to reject or accept the null hypothesis is made
during this step.This step wither uses critical approach method or p-value method.
Step 8: Express the conclusion in the context of the problem
HYPOTHESIS TESTING
4
My Prefer Method
There are two procedures for deciding whether to reject or accept the null hypothesis.
Based on the performing 8 steps for hypothesis testing, I prefer p-value method in deciding
whether to reject the null or not. I find p-value approach easier than critical value approach,
although both give the same result. I find it easier in making decisions regarding selecting the
correct hypothesis. A null hypothesis will always be rejected if the p-value is less than the
assumed significance level.
Perform the hypothesis test
The claim is that the average age of all patients admitted to the NLEX hospital is less
than 65 years of age. In order to test the claim, a single sample t-test was used.Also, it is
assumed that the data is normally distributed.
1. Null Hypothesis:µ=65
Alternative Hypothesis: µ <65 Here,µ is the average age of the patients being admitted to NLEX hospital. Since the claim is that the average age of all patients is less than 65 years of age, therefore, in this case, an alternative hypothesis is the claim. 2. The test is a left tailed test because the alternative hypothesis contains less than sign. 3. Since the population standard deviation is not known, therefore we will use a t-test for proving or disproving the claim. 4. Calculation of test Statistic Sample mean,m = 61.82 Sample standard deviation,s= 8.92 Sample size,n= 60 HYPOTHESIS TESTING Degree of freedom =n-1=59 Standard error of the sample,se =s/sqrt(n) = 8.92/sqrt(60) = 1.152 Test-statistic,t = (Sample mean ? Population claimed mean)/standard error = (61.8265)/1.152 =-2.76 t-value =-2.76 5.P-value = 0.0038,using t-table 6.Since it is a right-tailed test, therefore critical value at 0.05 significance level is 1.6711 obtained using Excel function, =T.INV(.05,59) 7.The decision is to reject the null since the p-value is less than the assumed significance level of 0.05. 8. Thus, it can be concluded that the average age of all patients admitted to the hospital with infectious disease is less than 65 years of age. 5 HYPOTHESIS TESTING 6 References Downing, D., & Clark, J. (2010). Business statistics. Hauppauge, NY: Barron's Educational Series. Lane, D. (2017). Steps in Hypothesis Testing. Onlinestatbook.com. Retrieved 21 January 2018, from http://onlinestatbook.com/2/logic_of_hypothesis_testing/steps.html ... Purchase answer to see full attachment

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