Category: Statistics homework help

 Instructions
Introduction:
One of the goals of this course is that you will be able to perform hypothesis tests. In this project, you will demonstrate your understanding of all the steps involved in testing a hypothesis test of μ when σ is unknown. Use the attachment for the Pearson Correlation Coefficient.
Directions:
Conduct the hypothesis test described further below. Write up the process and the results of the test in a professional-quality report using Microsoft Office. Include the following elements in your 1-2 page written report:
INTRODUCTION:
Describe the scenario and the reason why LEGO Group’s line manager should perform a hypothesis test.
BODY:
Include the following elements in the body of the report:
a) The name of the appropriate hypothesis test (e.g., “1 Sample Proportion Z test,” “1 Sample T-Test for Means”, etc.)
b) The null and alternative hypotheses. (Be sure to first define the parameter in context.)
c) Requirements check that justifies the use of the test:
i) Is the sample a simple random sample?
ii) Is the sample from a normal distribution, or does the Central Limit Theorem apply because ???? ≥ 30?
d) Give all the test details, including the sample statistic, the test statistics, the critical value, and the p-value.
e) Reject or fail to reject the null hypothesis
f) Report the conclusion of the hypothesis test in context.
g) Report and interpret the confidence interval estimate of the parameter in question
h) Weave in answers to any specific elements requested below.
4. CONCLUSION:
Write a brief conclusion to the report
5. After completing the report, save the Word document as a PDF and upload it to Data Analysis Project (KPA) dropbox on D2L.
SCENARIO:
The LEGO Group, an international company, makes the LEGO blocks that many of us have played with as kids. Many of its products require that the production process performs according to specifications. One of the products is Little People. The neck diameter of each of the Little People must be 0.5 inches so that it can be attached to the head properly. LEGO is interested in testing to see whether this process is performing according to specifications. If it is not functioning correctly, the LEGO Group will shut down the manufacturing process to fix the Little People machine.
The line manager takes a random sample of 40 Little People heads. The average diameter of the sampled necks is 0.48 inches, with a standard deviation of 0.05 inches. Is there sufficient evidence that the machine is not working correctly? Use a two-tailed hypothesis test with a significance level of α=0.02 to determine the answer.
Give the confidence interval estimate for the actual population neck size of Little People. Use a 98% confidence level so that it aligns with the hypothesis test in part 2.
Does “0.5 inches” appear in the confidence interval? Does the confidence interval estimate of the mean neck size, of Little People align with the conclusion of your hypothesis test? Explain why the two methods for estimating match or don’t.

 By the due date assigned, write a paper addressing the sections below of the research proposal.
Methodology
 Data Analysis Plans
 Describe plan for data analysis for demographic variables (descriptive statistical tests). Describe plan for data analysis of study variables (descriptive and inferential  statistical tests)

 
You’re a realtor with a client in the market for a 3+ bedroom home with at least 2 baths.  Randomly sample 10 homes from your original data set from Part A that meet these criteria.  Write a report that includes a linear regression model that predicts a home’s listing price based on its size (in square feet).  The use of EXCEL or other data software may be beneficial.
Write an introduction that includes the context of the data and precisely describes the sampling method used to achieve your random sample. Provide a data table that includes the 10 selected homes, their square footage, and their listing price. Calculate the mean and standard deviation for both square footage and price.
Create a scatterplot showing the association between the two variables. The scatterplot should include the least-squares line and a generic version of the regression equation.
Describe the association’s direction and form in context of the variables. Describe the strength of the association by providing a calculated correlation coefficient.
Provide a contextual version of the regression equation. Interpret the slope, intercept, and R2 of the model in context of the two variables.
Note any outliers or influential points in your scatterplot. Describe what might happen to your model if they were excluded.
Select one home from your list of 3+ bedroom, 2+ bathroom homes. Interpret the residual associated with this selection. Is the home a good deal, fair deal, or poor deal for your client?

 
Governing Article Discussion 1
Read the article “Managing Marijuana: The Role of Data-Driven Regulation” and the following:
https://ascend.aspeninstitute.org/an-evidence-based-approach-to-child-support/
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Briefly skim this article on how to report data with small numbers (pay attention to pp 2-6).
Review the guidance issued by the Federal Trade Commission on protecting personal data. 
Watch this Podcast: Privacy and Predictions
1. What did you find most interesting related to the use of data in the articles and podcasts?
2. Royse, Thyer, and Padgett discuss privacy on pp. 44-47 and outcome evaluations on pp 228-234 (chapter 9).  Pick one element of their privacy discussion and briefly describe it focusing on how it applies to an evaluation of program outcomes.  Without getting into specifics, how well does your agency protect the identities of people included in its data?
3. How useful are descriptive statistics to a program evaluator when the sample size is very small?      

In both for-profit and not-for-profit organizations, statistics are critical pieces of information that allow decision makers to steer the organization in directions that are in the organization’s best interest. Data is acquired from many sources, some within the organization, and some from outside the organization. The government tracks data on many different aspects of society (including industrial output). The following will guide your thinking about the uses of data and information.
Review the important themes within the sub question of each bullet point. The sub questions are designed to get you thinking about some of the important issues. Your response should provide a succinct synthesis of the key themes in a way that articulates a clear point, position, or conclusion supported by research.
You are analyzing the cross-store sales of a grocery store chain. As part of your analysis, you compute two measures of central tendency—mean and median. The mean sales are $358.4 million, and the median sales are $163.1 million (per store).
To quantify the average sales per store, evaluate which of the two measures would you use and why. Support your discussion with relevant examples, research, and rationale.
The final paragraph (three or four sentences) of your initial post should summarize the one or two key points that you are making in your initial response.
Submission Details
Your posting should be the equivalent of 1 to 2 single-spaced pages (500–1000 words) in length.
Since you are engaging in research, be sure to cite in the body of the post and add a reference list in APA format
  Comment on 2 student responses attached 

Question 2 [20]
The number of Golden Key candidates for at RBS of different ages in the 2023 academic year is shown in the table below.
Candidate age (years)
Number of Candidates
10 < 20 4 20 < 30 9 30 < 40 18 40 < 50 26 50 < 60 17 60 < 70 6 For these patients, determine the: 2.1 mean age of the candidates. (3) 2.2 modal age of the candidates. (3) 2.3 Median age of the candidates (4) 2.4 Determine the coefficient of variation and comment on your findings. (10) Question 5 [20] A market basket consists of three goods: apples, bananas, and oranges. The quantity and price of each good in the base period and the current period are given below. Quantity (2020) Price (2020) Quantity (2022) Price (2022) Apples 20 R2 25 R2.50 Bananas 30 R1 40 R1.20 Oranges 10 R3 15 R3.50 Calculate and interpret the following price and quantity indices. 5.1 Laspeyre Price Index (5) 5.2 Paasche Price Index (5) 5.3 Laspeyre Quantity Index (5) 5.4 Paasche Price Index (5)

 
Your goal for this assignment is to: Practice your problem-solving skill by answering questions about statistical concepts and the benefits and uses of data-driven decision-making.
Steps to Complete:
Step 1:
You would like to determine whether eating before bed influences sleep patterns. List each of the seven steps for conducting a statistical study.
Explain what you would do to complete each step.
Then, answer the questions below:

What is your hypothesis on this issue?
What type of data (quantitative or categorical) will you be looking for? What are some examples?
What methods would you use to gather information? Which sampling method would you use and why?
How would the results of the data influence decisions you might make about eating and sleeping?
How would we know if the results of the study are valid and reliable?
What questions would you ask to find out more about the quality of the data?
Why is it important to gather and report valid and reliable data?

Submission Instructions:
When you are ready to submit your completed Week 3 Assignment Template

 Write a 100 word minimum paragraph describing a real-life situation where correlation and regression might be used.
Explain the steps and the process involved in calculating the correlation and regression for your real-life situation in detail.
In order to receive credit, your paragraph must be in your own words and not simply cut and paste from a website.
Respond to at least one of your colleagues with a minimum of 30 words. 

Confidence Intervals
In everyday terms, a confidence interval is the range of values around a sample statistic (such as mean or proportion) within which clinicians can expect to get the same results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you ask yourself, “Will I get the same results if I use this research?”, you must address the precision of study findings, which is determined by the Confidence Interval. If the CI around the sample statistic is narrow, you can be confident you will get close to the same results if you implement the same research in your practice.
Consider the following example. Suppose that you did a systematic review of studies on the effect of tai chi exercise on sleep quality, and you found that tai chi affected sleep quality in older people. If, according to your study, you found the lower boundary of the CI to be .49, the study statistic to be 0.87, and the upper boundary to be 1.25, this would mean that each end limit is 0.38 from the sample statistic, which is a relatively narrow CI.
(UB + LB)/2 = Statistic [(1.25 + .49)/2 = .87]
Keep in mind that a mean difference of 0 indicates there is no difference; this CI does not contain 0. Therefore, the sample statistic is statistically significant and unlikely to occur by chance.
Because this was a systematic review, and tai chi exercise has been established from the studies you assessed as helping people sleep, based on the sample statistics and the CI, clinicians could now use your study and confidently include tai chi exercises among possible recommendations for patients who have difficulty sleeping.
Now you can apply your knowledge of CIs to create your own studies and make wise decisions about whether to base your patient care on a particular research finding.
Initial Post Instructions
Find an example of a confidence interval in the news, scholarly source or medical journal. Summarize the article/study. Does the article/study include the sample size and the level of confidence used to create the confidence interval? Explain what the confidence interval means in context of the news article or scholarly source.

Hello Professor and Class. 
For this article, I chose an article by The Wisconsin Department of Health Services explaining confidence interval studies. This study does an excellent job of putting these weeks’ lessons into simple laymen terms that helped me understand the concept.
“In 2005 the estimated percentage of current smokers among Wisconsin adults was 20.7%, with a confidence interval of +/- 1.1%. The estimated population of current smokers was 850,900.
First, calculate the range of the population confidence interval:
R = (1.1/20.7)*850,900 = 45,217 (or 45,200 rounded to the nearest 100)
Then calculate the confidence interval by applying the range to the estimated population:
CI = 850,900 +/- 45,200
In other words, there is a 95% probability that in 2005 the true number of adult smokers in Wisconsin fell within the range of 805,700 – 896,100 people.” (2023) 
By using confidence intervals this study demonstrates how confidence intervals can be used in this case for behavioral risk factors. So instead of asking every resident of the state they can take a sample size and work out the probability. It also shows how factors affect the size of the confidence interval. One is the desired confidence meaning a higher percentage such as 99% would lead to a wider interval. The second is the sample size used for the estimate the larger the size the smaller the confidence interval will be. 
References
Behavioral risk factor survey module: Confidence intervals around sample estimates. Wisconsin Department of Health Services. (2023, January 5). https://www.dhs.wisconsin.gov/wish/brfs/confidence-intervals.htm#:~:text=For%20example%2C%20in%202005%20the,(20.7%25%20%C2%B1%201.1%25).