complete phase 5 inferential statistics. see attachedThis week you will submit Phase 5, the final phase, of your course project. For Phase 5 of your

course project, you will want to review your instructors feedback from your Phase 4 submission and

make any necessary corrections. Remember if you have questions about the feedback to ask your

instructor for assistance.

Once you have made your corrections, you will make your final submission for the course project.

Below is a summary of the expectations for Phase 5 of the course project:

1. Introduce your scenario and data set.

Provide a brief overview of the scenario you are given above and the data set

that you will be analyzing.

Classify the variables in your data set.

Which variables are quantitative/qualitative?

Which variables are discrete/continuous?

Describe the level of measurement for each variable included in your

data set.

2. Discuss the importance of the Measures of Center and the Measures of Variation.

o What are the measures of center and why are they important?

o What are the measures of variation and why are they important?

3. Calculate the measures of center and measures of variation. Interpret your results in context of

the selected topic.

o Mean

o Median

o Mode

o Midrange

o Range

o Variance

o Standard Deviation

4. Discuss the importance of constructing confidence intervals for the population mean.

o What are confidence intervals?

o What is a point estimate?

o What is the best point estimate for the population mean? Explain.

o Why do we need confidence intervals?

5. Based on your selected topic, evaluate the following:

o

o

o

Find the best point estimate of the population mean.

Construct a 95\% confidence interval for the population mean. Assume that your data is

normally distributed and σ is unknown.

Please show your work for the construction of this confidence interval and be

sure to use the Equation Editor to format your equations.

Write a statement that correctly interprets the confidence interval in context of your

selected topic.

6. Based on your selected topic, evaluate the following:

o Find the best point estimate of the population mean.

o Construct a 99\% confidence interval for the population mean. Assume that your data is

normally distributed and σ is unknown.

Please show your work for the construction of this confidence interval and be

sure to use the Equation Editor to format your equations.

o Write a statement that correctly interprets the confidence interval in context of your

selected topic.

o

Compare and contrast your findings for the 95\% and 99\% confidence interval.

Did you notice any changes in your interval estimate? Explain.

What conclusion(s) can be drawn about your interval estimates when the

confidence level is increased? Explain.

8. Discuss the process for hypothesis testing.

o Discuss the 8 steps of hypothesis testing?

o When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value

method or Critical Value method? Why?

9. Perform the hypothesis test.

o If you selected Option 1:

Original Claim: The average salary for all jobs in Minnesota is less than

$65,000.

Test the claim using α = 0.05 and assume your data is normally distributed and σ

is unknown.

o

If you selected Option 2:

Original Claim: The average age of all patients admitted to the hospital with

infectious diseases is less than 65 years of age.

Test the claim using α = 0.05 and assume your data is normally distributed and σ

is unknown.

o

Based on your selected topic, answer the following:

1. Write the null and alternative hypothesis symbolically and identify which

hypothesis is the claim.

2. Is the test two-tailed, left-tailed, or right-tailed? Explain.

3. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain.

4. What is the value of the test-statistic? What is the P-value?

What is the critical value?

5. What is your decision; reject the null or do not reject the null?

a. Explain why you made your decision including the results for your pvalue and the critical value.

6. State the final conclusion in non-technical terms.

10. Conclusion

o Recap your ideas by summarizing the information presented in context of your chosen

scenario.

Please be sure to show all of your work and use the Equation Editor to format your equations.

This assignment should be formatted using APA guidelines and a minimum of 2 pages in

length

Jeffery, to obtain a better grade next week, you need to add/correct

the following:

-phase 1: the age is not a quantitative variable, but the number

assigned to a patient is; the value of the midrange is not accurate (it

is 55.5); try to give an interpretation to your obtained values;

-phase 2: when you apply the formula to find the margin of errors

you make 2 mistakes: the samples standard deviation is 8.92, not

8.3; you need to divide the standard deviation by the square root of

60 according to the formula; also, you used the normal distribution

and took the values from the z-table, but you need to use the Student

t distribution because sigma is unknown; in other words, you must

use the t-table;

Good luck,

Alin Tomoiaga

STATISTICS

1

Statistics

Jeff L Clayborn

Rasmussen College

12/09/2016

STATISTICS

2

Part 1

The hospital has been debating on whether age of a patient influences the rate at which

one acquires infectious diseases. I will be analyzing data on the age of patients who have

contracted infectious diseases.

In the data that is employed in analysis, infectious diseases in the qualitative variable

while the age of the patient is the quantitative variable.

In the used data, the age of patients is discrete such as 60 and 40 years of age with no

decimal places. Similarly, the number of patients is discrete variable in the data set .The data that

is used has no continuous data apart from in the measures of center and variation.

In terms of level of measurement, age and numbers of patients are ordinal while

infectious diseases is nominal.

Part 2

Measures of center is that value which is found the at middle of a given set of data .The

measures of center play a significant role in the society since many people always want to

identify an average of a given set of data .For example, the average number ,speed as well as age.

Most common measures of center used are mean, median and mode.

Measures of variations are the quantities which show the amount of variations in a given

random variable .Variation is the spread between data. Measures of variation are important in

that they indicate that degree in which a given set of data spreads about a specified average value

.The measures of variance include: range, variance, standard deviation as well as sum of squares.

Part 3

STATISTICS

Excel

Part 4

Confidence interval is the given range of values that are defined in that there is a given

probability that proves that values of a parameter is found within them.

Point estimate is a distinct value which is an estimate of population parameter.

The best point estimate of a population mean is the sample mean since it is unbiased.

We need confidence interval in statistics to determine values of an unknown population

parameters that one might be looking for.

Part 5

The best point estimate of a population mean is a sample mean

Using 95 \% confidence level, our confidence interval is

= 61.82 +- (1.96×8.30)

= 61.82- 16.019< µ < 61.82+ 16.019
= 45.801 < µ 30, the data is normally distributed the sample mean of 61.82 is the best
estimate of the population of the patients with infectious diseases.
The 0.99 confidence interval means that α = 0.01, hence Z = 2.576
Confidence interval is
𝑋ֿ ± 𝑍 ∗ б
Sample mean + or – Z x Sample standard deviation
Sample standard deviation = 8.30
= 61.82 +- (2.576 x8.30)
= 61.82- 21.3808< µ < 61.82+ 21.3808
STATISTICS
5
= 40.4392 < µ < 83.2008
The above confidence interval means that if we were to choose other small samples of 60
patients from the population of patients, we are 99\% confident that the population mean of their
age will lie between 40 years and 83 years of age.
Part 7
From the above two calculations of the calculating confidence interval, we can conclude
that the confidence interval has reduced as we decreased the confidence level.
The more we increase the confidence level the more the confidence interval increase .The
main reason is that one increases their confidence that that contains the mean of the population.
Part 8
Hypothesis testing is a statistical process used to test whether there is sufficient statistical
evidence to support a claim about a certain population parameter.
Steps involved in hypothesis testing include:
a) Step 1: formulate a null and alternate hypothesis
This step involves determining or predicting what the expected outcome of the research
will be.
b) Step 2: Determine the significance level ( alpha level)
STATISTICS
6
The alpha level gives the probability of committing a type I error. This step thus involves
coming up with an appropriate alpha level (maximum allowable error) depending on the
topic of investigation.
c) Step 3: Data collection and calculation of descriptive statistics
This step involving collecting the necessary data required to test the claim and calculating
the descriptive statistics. Measures of dispersion and central tendency are useful in
calculating the test statistic.
d) Step 4: Determine the test to use
Hypothesis testing mainly involves use of t tests or z tests. In this step, one determines
what test is appropriate to use. Z tests are used when the population standard deviation is
known and when the sample size is large. T tests are used when the population standard
deviation is unknown and when the underlying population is normally distributed.
e) Step5:Determiningthe critical values and the rejection
Depending on the test used, one will determine the critical values, depending on whether
the test is one tail or two tailed. Based on either the significance level, or critical values
one will determine the rejection region
f) Step 6: Calculate the test statistic.
For a z test
Z statistic = (x bar – u)/(𝛔/√n)
For a t test
T statistic = (x bar – u)/(s/√n)
g) Step 7: Determine the p value.
Based on the test statistic calculated, one should calculate the p value.
STATISTICS
h) Step8:Makea decision and state the conclusion
In this final step, one makes a decision on whether to reject or not reject the null
hypothesis and makes the appropriate conclusion.
In an 8 step hypothesis test, one makes use of both critical values and p values to make the
statistical decision and conclusion. This ensures that the test was correct done and avoids risk of
error.
Part 9
Hypothesis testing for an infectious disease at NCLEX Memorial Hospital
In this paper, we will be testing the claim that the average age of all patients admitted to the
hospital with infectious diseases is less than 65 years of age. We will be testing this claim at the
0.05 significance level
The Null and alternate Hypothesis will be:
Ho: u = 65
Ha: u < 65
(claim)
This kind of hypothesis testing is a left-tailed hypothesis. This is because in the alternate
hypothesis we will be determining whether the mean age is less than 65 years. The p value to
check for will be the area on the left tail of the test statistic.
7
STATISTICS
8
For our case, we will use t test. This is because the population standard deviation (𝛔) is
unknown.
Test statistic
T statistic = (x bar – u)/ (s/ √n)
From the data:
Mean (x bar)
61.816667
Standard Error(s/√n)
1.1521269
Standard Deviation (s)
8.9243367
Count (n)
60
T statistic = (61.8167 – 65)/ 1.1521
= -2.763
P value
To determine p value we first need to get the degrees of freedom.
Degrees of freedom (df) = n – 1 = 60 – 1 = 59
We will then check at t tables for p value associated with the test statistic
P (t < -2.763) at 59 df = 0.0038
STATISTICS
9
P value = 0.0038
Critical value
To determine the critical value, we need to check t tables for the t value associated with the
significance level at the current degrees of freedom.
In our case we will check for t value associated with 0.05 left-tail probability at 59 df
T critical = -1.671
Critical region = any t value < -1.671
Decision rule and Conclusion
We reject the null when p value is less than significance level or when the test statistic lies within
the critical region.
From the test above, the p value (0.0038) is less than the 0.05 significance level. The t statistic (2.763) lies in the critical region. Based on this, our decision will be to reject the null hypothesis.
We thus conclude that there is sufficient evidence to support the claim that the average age of all
patients admitted to the hospital with infectious diseases is less than 65 years of age
Conclusion
Hypothesis testing is a great method for determining whether claims about a certain population
are statistically significant (valid) or not.
STATISTICS
10
Part 10
In summary, data analyst who wants to analyse data must have knowledge on how to
calculate sample size. Similarly, they have to have knowledge on point estimates of population
parameters and come up with best point estimates which are unbiased. Notably, they have to
know how to carry out hypothesis testing of a given simple before coming up with conclusions
and decision making .They should also be aware that when sample size is big while the standard
error is small, the confidence interval will be narrow. Therefore, the data analysts should also
look at measures of center and variability of a given set of data before coming up with a solution.
STATISTICS
11
References
Morse, J. M. (2000). Determining sample size. Qualitative health research, 10(1), 3-5.
Nakagawa, S., & Cuthill, I. C. (2007). Effect size, confidence interval and statistical
significance: a practical guide for biologists. Biological Reviews, 82(4), 591-605.
Pond, S. L. K., & Muse, S. V. (2005). HyPhy: hypothesis testing using phylogenies. In Statistical
methods in molecular evolution (pp. 125-181). Springer New York.
Zhao, Y. G., & Ono, T. (2000). New point estimates for probability moments. Journal of
Engineering Mechanics, 126(4), 433-436.
Running head: HYPOTHESIS TESTING
1
Infectious disease hypothesis testing
Jeff L Clayborn
12/1/2016
Rasmussen College
HYPOTHESIS TESTING
2
Introduction
Hypothesis testing is a statistical process used to test whether there is sufficient statistical
evidence to support a claim about a certain population parameter.
Steps involved in hypothesis testing include:
a) Step 1: formulate a null and alternate hypothesis
This step involves determining or predicting what the expected outcome of the
research will be.
b) Step 2: Determine the significance level ( alpha level)
The alpha level gives the probability of committing a type I error. This step thus
involves coming up with an appropriate alpha level (maximum allowable error)
depending on the topic of investigation.
c) Step 3: Data collection and calculation of descriptive statistics
This step involving collecting the necessary data required to test the claim and
calculating the descriptive statistics. Measures of dispersion and central tendency are
useful in calculating the test statistic.
d) Step 4: Determine the test to use
Hypothesis testing mainly involves use of t tests or z tests. In this step, one determines
what test is appropriate to use. Z tests are used when the population standard deviation
is known and when the sample size is large. T tests are used when the population
standard deviation is unknown and when the underlying population is normally
distributed.
e) Step5:Determiningthe critical values and the rejection
Depending on the test used, one will determine the critical values, depending on
whether the test is one tail or two tailed. Based on either the significance level, or
critical values one will determine the rejection region
HYPOTHESIS TESTING
3
f) Step 6: Calculate the test statistic.
For a z test
Z statistic = ( x bar – u)/(𝛔/√n)
For a t test
T statistic = ( x bar – u)/(s/√n)
g) Step 7: Determine the p value.
Based on the test statistic calculated, one should calculate the p value.
h) Step8:Makea decision and state the conclusion
In this final step, one makes a decision on whether to reject or not reject the null
hypothesis and makes the appropriate conclusion.
In an 8 step hypothesis test, one makes use of both critical values and p values to make the
statistical decision and conclusion. This ensures that the test was correct done and avoids risk
of error.
Hypothesis testing for an infectious disease at NCLEX Memorial Hospital
In this paper, we will be testing the claim that the average age of all patients admitted to the
hospital with infectious diseases is less than 65 years of age. We will be testing this claim at
the 0.05 significance level
The Null and alternate Hypothesis will be:
Ho: u = 65
Ha: u < 65
(claim)
This kind of hypothesis testing is a left-tailed hypothesis. This is because in the alternate
hypothesis we will be determining whether the mean age is less than 65 years. The p value to
check for will be the area on the left tail of the test statistic.
For our case, we will use t test. This is because the population standard deviation (𝛔) is
unknown.
Test statistic
HYPOTHESIS TESTING
4
T statistic = ( x bar – u)/ (s/ √n)
From the data:
Mean (x bar)
Standard Error(s/√n)
Standard Deviation (s)
Count (n)
61.816667
1.1521269
8.9243367
60
T statistic = (61.8167 – 65)/ 1.1521
= -2.763
P value
To determine p value we first need to get the degrees of freedom.
Degrees of freedom (df) = n – 1 = 60 – 1 = 59
We will then check at t tables for p value associated with the test statistic
P (t < -2.763) at 59 df = 0.0038
P value = 0.0038
Critical value
To determine the critical value, we need to check t tables for the t value associated with the
significance level at the current degrees of freedom.
In our case we will check for t value associated with 0.05 left-tail probability at 59 df
T critical = -1.671
Critical region = any t value < -1.671
Decision rule and Conclusion
We reject the null when p value is less than significance level or when the test statistic lies
within the critical region.
From the test above, the p value (0.0038) is less than the 0.05 significance level. The t statistic
(-2.763) lies in the critical region. Based on this, our decision will be to reject the null
hypothesis.
We thus conclude that there is sufficient evidence to support the claim that the average age of
all patients admitted to the hospital with infectious diseases is less than 65 years of age
HYPOTHESIS TESTING
Conclusion
Hypothesis testing is a great method for determining whether claims about a certain
population are statistically significant (valid) or not.
5
ESTIMATES AND SAMPLE SIZES
1
Estimates and Sample Sizes
Jeff L Clayborn
Rasmussen College Inferential Statistics
11/25/2016
ESTIMATES AND SAMPLE SIZES
2
Estimates and Sample Size
Part A
Population parameters has two types of estimates: point estimates as well as confidence
interval .Confidence interval is a range of figures containing population mean of a given time of
either 95\% 0r 99\%.Similarly one can define confidence interval as a range of many values which
are used in estimating the actual value of a parameter of a given population .The parameters may
include the proportion of the population , mean of the population as well as the mean of the
population .Confidence intervals are crucial since they give more information about a given
estimate for a population. Confidence interval goes hand in hand with the confidence level. The
confidence level shows the probability of the confidence interval to contain the population
parameter of a given sample. Confidence level include, 95\% which has a critical z value of 1.96,
99\%, 98 \% as well as 90 \%.
On the other hand, a point estimate of a given parameter of a population is a value that is
used to estimate the actual parameter of that population .For example the mean of a given sample
estimates the mean of the whole population .The best point estimate for population mean is the
sample mean since it reflects the mean of the population .Confidence intervals are essential since
they are used by statisticians in expressing the degree or extent of uncertainty which is connected
to a given sample data.
Part B
The best point estimate of a population mean is a sample mean
ESTIMATES AND SAMPLE SIZES
3
For example sample mean of age of the patients with infectious disease of 60 patients is 61.82
and the sample standard deviation is 8.30.
Since n =60 which is > 30, the data is normally distributed the sample mean of 61.82 is the best

estimate of the population of the patients with infectious diseases.

The 0.99 confidence interval means that α = 0.01, hence Z = 2.576

Confidence interval is

𝑋ֿ ± 𝑍 ∗ б

Sample mean + or – Z x Sample standard deviation

Sample standard deviation = 8.30

= 61.82 +- (2.576 x8.30)

= 61.82- 21.3808< µ < 61.82+ 21.3808
= 40.4392 < µ < 83.2008
The above confidence interval means that if we were to choose other small samples of 60
patients from the population of patients, we are 99\% confident that the population mean of their
age will lie between 40 years and 83 years of age.
Part C
ESTIMATES AND SAMPLE SIZES
4
Using 95 \% confidence level, our confidence interval is
= 61.82 +- (1.96x8.30)
= 61.82- 16.019< µ < 61.82+ 16.019
= 45.801 < µ
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