Expert answer:Need help with Module 4 of a statistics project.

Expert answer:This week you will begin working on Phase 4 of your course project. For Phase 4 of your course project, you will want to review your instructor’s feedback from your Phase 1, Phase 2, and Phase 3 submissions to 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 compile your information from Phase 1, Phase 2, Phase 3 and your final conclusion into one submission and submit this as your rough draft for Phase 4 of the course project. Below is a summary of the expectations for Phase 4 of the course project: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.Discuss the importance of the Measures of Center and the Measures of Variation.What are the measures of center and why are they important?What are the measures of variation and why are they important?Calculate the measures of center and measures of variation. Interpret your results in context of the selected topic.MeanMedianModeMidrangeRangeVarianceStandard DeviantionDiscuss the importance of constructing confidence intervals for the population mean.What are confidence intervals?What is a point estimate?What is the best point estimate for the population mean? Explain.Why do we need confidence intervals?Based on your selected topic, evaluate the following: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.Based on your selected topic, evaluate the following:Find the best point estimate of the population mean.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.Write a statement that correctly interprets the confidence interval in context of your selected topic.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.Discuss the process for hypothesis testing.Discuss the 8 steps of hypothesis testing?When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value method or Critical Value method? Why?Perform the hypothesis test.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.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.Based on your selected topic, answer the following:Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim.Is the test two-tailed, left-tailed, or right-tailed? Explain.Which test statistic will you use for your hypothesis test; z-test or t-test? Explain.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?Explain why you made your decision including the results for your p-value and the critical value.State the final conclusion in non-technical terms.ConclusionI’ve attached assignments turned in for weeks 1-3. week 1 Needs work I got a B-, week 2 I got A, week 3 another B-.
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Running Header: COURSE PROJECT – PHASE 3
Course Project – Phase 3
Linda Sharum
Rasmussen College
Author Note
This paper is being submitted on December 3, 2017, for Alin Tomoiaga’s STA3215
Inferential Statistics and Analytics course.
1
COURSE PROJECT – PHASE 3
2
Course Project – Phase 3
The Hypothesis Testing is a statistical test used to determine whether the hypothesis
assumed for the sample of data stands true for the entire population or not. Simply, the
hypothesis is an assumption which is tested to determine the relationship between two data sets.
In hypothesis testing, two opposing hypotheses about a population are formed Viz. Null
Hypothesis (H0) and Alternative Hypothesis (H1). The Null hypothesis is the statement which
asserts that there is no difference between the sample statistic and population parameter and is
the one which is tested, while the alternative hypothesis is the statement which stands true if the
null hypothesis is rejected (Businessjargons, 2017).
Steps Hypothesis Testing
Step 1: Identify the claim to be tested and express it in symbolic form. Stating of the null
hypothesis, Ho, and the alternative hypothesis Ha. The null hypothesis refers to the negation of
what the researcher is trying to verify while alternative hypothesis represents what the
investigator is working to prove (Triola, 2018).
Step 2: Give symbolic form. Offer symbolic form that must be true when the original claim is
false. Stating the size of the sample that represent the number of things used to make the
conclusion and decision thereafter (Triola, 2018).
Step 3: Identify null and alternative hypothesis. Consider two symbolic expressions obtained so
far. Null hypothesis Ho and alternative hypothesis Ha (Triola, 2018).
Step 4: Select significance level. Select the significance level A based on the seriousness of a
type I error. Make a small if the consequences of rejecting a true Ho are severe (Triola, 2018).
COURSE PROJECT – PHASE 3
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Step 5: Identify the Test Statistic Identify the test statistic that is relevant to the test and
determine its sampling distribution (such as normal, t, chi-square) (Triola, 2018).
Step 6: Find Values: P-value: find the value of the test statistic and the P-value. Draw a graph
and show the test statistic and P-value. Find the value of the test statistic and the critical values.
Draw a graph showing the test statistic, critical value(s) and critical region (Triola, 2018).
Step 7: Make a Decision: Reject Ho if P-value < a. or fail to reject Ho if P-value > a. Reject Ho if
the test statistic is in the critical region. • Fail to reject H0 if the test statistic is not in the critical
region. Comparing the values of the test statistic and critical value of the test would enable one to
decide whether to reject the theory being tested or fail to reject Ho (Triola, 2018).
Step 8: Restate Decision in Nontechnical Terms Restate this previous decision in simple
nontechnical terms, and address the original claim. Making the final conclusion by either
rejecting Ho or failing to reject the same supposition (Triola, 2018).
The P-value or Critical Value
Both values give the same result when conducting hypothesis testing. I prefer p-value as
the best approach since it only requires the calculation of one value in to conduct the test. On the
contrast, the critical value requires one to compute both the test statistic and then proceed to find
the tabulated value that corresponds to a given significant level.
Hypothesis Testing of Salaries
1. H0 = $65000
Ha > $65000
COURSE PROJECT – PHASE 3
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2. The hypothesis is a right tailed test, which implies that the critical region is only on one
side of the standard normal distribution. The null hypothesis rejection area is only one
side.
3. The test statistic that will be used for this hypothesis test is t-test. This is because the
variance of the normal distribution is unknown.
4. T-test statistics calculation
−
t =
⁄
√
=
62306−65000 −2694
=
19149⁄
1004
√364
= -2.6833, Where x is the sample mean, u is the population
mean, s is the standard deviation and n is sample size.
5. P-value: The P value, or calculated probability, is the probability of finding the observed,
or more extreme, results when the null hypothesis Ho of a study question is true – the
definition of ‘extreme’ depends on how the hypothesis is being tested. P-value is
calculated using the test statistic calculated from the samples, the assumed distribution,
and the type of test being done (lower-tailed test, upper-tailed test, or two-tailed test)
(Triola, 2018).
− 62306−65000 −2694
= 19149
=
1004
⁄
⁄
√
√364
Z=
= -2.6833
=1- ∅(Zo)=1-(-0.615) = 1.615
6. Critical Value: A critical value is the point (or points) on the scale of the test statistic
beyond which we reject the null hypothesis, and is derived from the level of significance
α of the test. Hypothesis tests are often done as such: calculate test statistics, calculate pvalue of test statistic, then compare p-value to the significance level. However, you can
COURSE PROJECT – PHASE 3
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also do hypothesis tests as such: calculate test statistic, calculate critical value(s) based on
the significance level, then compare test statistic to critical value (Triola, 2018).
T0.05,363 = 1.615, The critical value is obtained from the t tables
7. Since t= 2.6833 > 1.615, the null supposition is rejected and then conclude that the
salaries mean is significantly greater than $65,000 at 95% level of confidence.
8. The average salary for all jobs in Minnesota is less than $65,000 for different job
categories.
COURSE PROJECT – PHASE 3
6
References
Hypothesis Testing. (n.d.). Retrieved December 2, 2017, from

Hypothesis Testing

Triola, M. F. (2018). Elementary Statistics, 13th Edition. [Bookshelf Ambassadored]. Retrieved
from https://ambassadored.vitalsource.com/#/books/9780134464244/
Running head: COURSE PROJECT-PHASE 1
1
Course Project – Phase 1
Linda Sharum
Rasmussen College
Author Note
This paper is being submitted on November 18, 2017, for Alin Tomoiaga’s STA3215
Inferential Statistics and Analytics course.
COURSE PROJECT-PHASE 1
2
The scenario and data set
A major client of our company is interested in the salary distributions of jobs in the
state of Minnesota that range from $40,000 to $120,000 per year. Research and analysis will
be performed using the data set consisting of 364 records from by the Bureau of Labor
Statistics that was provided by our client. We were given a listing of the jobs by title and the
salaries for each job. Quick turnaround of the was requested therefore, this project has been
allocated priority in completion.
Classification of the variables in the data set
Job titles or position categories are qualitative variables while the quantitative
variables are the amount of salary per job title. Qualitative variables assist in determining
correlation between dependent variables. Discrete variables are the different types of jobs and
amount of salary per year. The analysis found no continuous variables for the provided data
set. The discrete variables provide straightforward statistical analysis of the workers. They
provide the specific round of data that is easy calculate and incorporate in the analysis.
Continuous variables require the findings of a particular set of values, in this case salaries for
each employee. There were three hundred and sixty-four jobs in the provided data set.
Salaries provided in the data set is represented in annual salary.
Significance of the measures of variation and central tendencies
The measures of central tendencies are those values found in the middle or centers of
the given data set. They include mode, mean, midrange and median. These measures are
important since they are the most used descriptive statistics one can easily obtain. Central
tendencies provide the individuals with ideas on the standard and common solutions. Mean
provides the average of the total salary of the jobs per people, the mode provides the
recurrent salary for the individual employees. It shows pay categories for a given group of
employees according to their working experience, education, and the level of promotion
COURSE PROJECT-PHASE 1
3
within the company (Rouse, 2017). Median provides the average salary scale for the workers
and the employers; it represents the wage scale range of the workers. This information is the
determinant used in hiring new employees.
Calculations of measures of central tendencies and variations, result interpretation
•
Mode =46,100
•
Median=56,520
•
Mean =62,300
•
Range =79,680
•
Midrange=80,010
•
Standard deviation=19149.2138
•
Variance=36669
Analytics
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
62306.12637
1003.691526
56520
46100
19149.21386
366692391.3
0.258251186
1.028918626
79680
40170
119850
22679430
364
COURSE PROJECT-PHASE 1
4
Conclusion
After research and analysis, the salary distributions for the Minnesota, the study found
that the minimum salary of workers in Minnesota using this data set of information is
$40,170 with the maximum amount being $119,850 for all the three hundred and sixty-four
jobs, with the average salary being $62,306. The most common salary for the workers falls in
the range from $40,170 to $64,070. Only twenty-six jobs titles fell in the range of $95,600119,800.
COURSE PROJECT-PHASE 1
5
References
Rouse, M. (n.d.). statistical mean, median, mode and range. Retrieved November 18, 2017,
from http://searchdatacenter.techtarget.com/definition/statistical-mean-median-modeand-range
Running Head: COURSE PROJECT – PHASE 2
Course Project – Phase 2
Linda Sharum
Rasmussen College
Author Note
This paper is being submitted on November 26, 2017, for Alin Tomoiaga’s STA3215
Inferential Statistics and Analytics course.
1
COURSE PROJECT – PHASE
2
Course Project – Phase 2
When conducting research or doing a survey it is generally accepted to use a sample of
the population since it is impossible to include the entire population in a research project not to
mention expensive. A sample number of people or data is used to represent the whole. Using this
method does leave exposure to variations because it does not define how good our estimate truly
represents the whole. We can use a population group of fifty people and get a mean population.
If we did the same study with fifty different people we could most likely get a different mean
population. Confidence intervals are important because they allow researchers to weigh their
variations to make better decisions; in essence confidence intervals are used to reduce risk.
Confidence intervals recognize the variation risks, consider the sample size and take into account
the variations in the population, ultimately including a range in which the real values lie
(Hochster, 2015).
Confidence interval (CI)– is a range of numbers assumed to include the true value of the
population parameter. CI contains the population mean or the center of the parameter. The two
numbers that make up the lower and upper ends of the confidence interval are called the lower
and upper confidence limits. CI’s are usually measured in a percent that will contain the
population mean a specified proportion of the time, usually either 95% or 99% of the time. If
sample tests were repeated, the 95% confidence interval computed for each sample, 95% of the
intervals would contain the population mean. Oppositely, 5% of the intervals would not contain
the population mean (Jarrett, 2011).
Point estimate – is a single number that is used to estimate an unknown population parameter. A
point estimate is not an accurate because we don’t know how right or wrong it is and we cannot
COURSE PROJECT – PHASE
3
be certain of the estimates accuracy. In general, point estimate is the act of choosing a parameter
which is the best guess of the true parameter, or the estimate (Statlect, 2017).
Point estimate for the population
Considering the definition of point estimate the best point estimate would be the sample
mean of the salaries of the various job groups. The mean of the population data is $62,306.13.
This is feasible because the population mean contains consistencies and can be approximated by
the normal distribution. It is also sufficient for large sample.
Best point estimate
Mean, µ =
∑
∑
Where SX is the total amount of salaries disbursed
S is the total number of job groups (the size of the population.)
Mean, µ =
$ 22,679,430
364
= $62,306.13
Constructing confidence intervals
At 95% confidence level.
Interval estimate = point estimate ± test statistic × standard error.
Interval estimate for µ = Ẋ ± Z

√
COURSE PROJECT – PHASE
4
Where; Ẋ is the point estimate
Z is the test statistic

√
Is the standard error.
Ẋ= $62,306.13
For large samples (n˃30)
Z = at 95%, ∝=0.05. Table area = 0.5-0.025 = 0.475. Therefore, from the standard normal
distribution tables Z=1.96
Interval estimate for µ = Ẋ ± Z

√
= $62,306.13± 1.96 ×
19,149.214
√364
= $62,306.13± 1,967.23
= [60,338.89, 64,273.36]
Thus 60,338.89< µ < 64,273.36 At 99% confidence level. ∝ = 0.01, from the standard normal tables Z= 2.58 Interval estimate for µ = Ẋ ± Z √ = $62,306.13± 2.58 × = $62,306.13± 2,589.52 = [59,716.60, 64,895.65] Thus 59,716.60< µ < 64,895.65 19,149.214 √364 COURSE PROJECT – PHASE The interpretation of the confidence interval can be summarized that we are 95% confident that the mean salary of the workers in different job groups who work in the company is between $60,338.89 and $64,273.36. At 99%, it means that we are 99% confident that the mean salary of the workers in different job groups in the company lies between $59,716.60 and $64,895.65. There is difference between the two confidence intervals at 95% and 99%. At 95% there is a small confidence interval as compared to 99% large confidence interval. This difference is contributed by the confidence level. This statement does not mean the probability that the mean salary of the entire population falls within the interval established from this one sample is 0.99. Instead, it means that if we select many random samples of the same size and calculate a confidence interval for each of these samples then in about 99% of these cases, the population mean will lie within that interval. Same case will apply at 95% confidence level. 5 COURSE PROJECT – PHASE 6 References Hochster, M., PhD. (2015, July 22). What is a confidence interval in layman's terms? Retrieved from https://www.quora.com/What-is-a-confidence-interval-in-laymans-terms Jarrett, C. (2011, November 7). What Is a Confidence Interval and Why Would You Want One? Retrieved from https://www.uxmatters.com/mt/archives/2011/11/what-is-a-confidenceinterval-and-why-would-you-want-one.php Point estimation. (n.d.). Retrieved November 23, 2017, from https://www.statlect.com/fundamentals-of-statistics/point-estimation Rumsey, D. J. (n.d.). How to Calculate a Confidence Interval for a Population Mean When You Know Its Standard Deviation. Retrieved from http://www.dummies.com/education/math/statistics/how-to-calculate-a-confidenceinterval-for-a-population-mean-when-you-know-its-standard-deviation/ ... Purchase answer to see full attachment

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