Spring 2020 Semester Project Detailed Instructions

Statcrunch is needed for this project please let me know so that I can give you my login info so that you can have access to the Data needed.

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Document Format: You must submit your project report in a single file through Canvas. The

acceptable formats are Microsoft Word (*.xlsx) or PDF (*.pdf) – no exceptions. The submission

page is in the Semester Project module. Projects submitted in multiple parts, in a format other than

Word or PDF, or via email/hardcopy will be rejected.

Style Requirements: The Semester Project module contains a sample project that would

receive a 100% grade. Your report should be formatted similarly.

− The first page of your report must be a title page containing your name, the course and

section number, the title “Semester Project,” and the submission date.

− Use a font suitable for an official business document. Any standard typeface is

acceptable as long as it is readable and presents a professional appearance (Calibri and

Times New Roman are good examples, but not the only possibilities). The size should

be no smaller than 12 points, and the color should be black.

− Do not include any borders, decorative images/illustrations, or watermarking.

− Embed all graphics directly into your project file. I will not accept separate files

containing graphics.

Data Set: All students will use the same data set: Spring 2020 Semester Project Raw Data. The

data set is located in the StatCrunch MTH 245 Homework Group. The data come from a

Stellenbosch University (South Africa) master’s thesis that studied blood chemistry in Type 2

diabetic patients. The variables of interest are random blood glucose (RBG) (measured in

millimoles per deciliter) and glycosylated hemoglobin (HBA1C) (measured as a percentage of

total red blood cells).

Technology Requirements: Except where required to build graphs or charts, all numerical

calculations must be performed using StatCrunch. Do not use a graphing calculator, Excel,

standard normal tables, or any other method for your numerical calculations.

Graphics Requirements: All graphics must be constructed using StatCrunch, Excel, or other

computer-based graphics program. Hand-drawn plots, cell phone pictures of graphics, etc., are

not acceptable. All graphics must include an informative title and (except for boxplots) correct

labels for both axes. Orient all boxplots horizontally.

Rounding Rules: In Section 1 histograms, round all upper and lower class bounds to three

decimal places. In the remaining sections, round all calculated sample statistics to four decimal

places and all p-values to three decimal places. Add trailing zeroes to any rounded value as

needed.

Required Content: Organize your report in five separate sections using the following numbers

and titles. The required elements for each section are as follows:

Section 1 – Visual Data Assessment. Create a histogram for each variable of interest RBG and

HBA1C. For RBG, use a “Start at:” value of 0.000 and a “Width:” value of 5.000; for HBA1C,

use a “Start at:” value of 2.000 and a “Width:” value of 2.000. It is not necessary to display

frequency counts above the bars. For each histogram, include a paragraph that answers

each of the following questions:

a. Is the histogram symmetric, left-skewed, or right-skewed?

b. How many peaks does the histogram have, and in which class(es) are they located

(must include the correct lower and upper bounds for each class listed)?

c. Does the histogram have any gaps between classes? If so, where are they?

Section 2 – Descriptive Statistics.

a. For each variable, find the mean, range, variance, standard deviation, and five-number summary. Display these numbers in a format that is easy to understand.

b. Construct a regular boxplot for each variable. For each boxplot, include a brief

statement containing an assessment of whether the data appear to be symmetric,

left-skewed, or right-skewed.

c. For each variable, construct a modified boxplot and use it to identify potential

outliers. If any exist, list them by value; if none exist, say so.

Section 3 – Confidence Intervals. Construct a 95% confidence interval for the mean μ of each

variable (two intervals total). Use the algebraic format for each interval (𝐿𝐿𝐿𝐿𝐿𝐿 < 𝜇𝜇 < 𝑈𝑈𝑈𝑈𝑈𝑈). State

the distribution you used for each interval (𝑡𝑡 or normal).

Section 4 – Hypothesis Test. Using the p-value method, conduct a formal hypothesis test of

the claim that the mean RBG of Type 2 diabetics is 13.5 mmol/dl or higher. Use 𝛼𝛼 = 0.01.

Include the following in your written summary of the results:

a. Your null and alternate hypotheses in the proper format using standard notation.

b. The type of distribution you used (𝑡𝑡 or normal).

c. The p-value and its logical relationship to 𝛼𝛼 (≤ or >).

d. Your decision regarding the null hypothesis: reject or fail to reject.

e. A statement interpreting your decision: reject/fail to reject (or support/fail to

support) the original claim that the mean RBG of Type 2 diabetics is 13.5 mmol/dl or

higher.

Note: Section 4 only applies to RBG. There is no hypothesis test related to HBA1C.

Section 5 – Correlation/Regression Analysis.

a. Construct a linear regression model with RBC as the predictor and HBA1C as the

response. State the equation incorrect algebraic format as shown in the course notes.

b. Create a scatter plot of the data with a plot of the least-squares line included.

(StatCrunch should generate this when you calculated the model in 5a.) The plot

must include an informative title and correct labels for both axes.

c. Use the coefficient of determination to identify the percentage of the variation in

HBA1C explained by the variation in RBC.

d. Identify the following points (list them as ordered pairs in the form (RBC, HBA1C)).

If none exist, say so.

1) Outliers (all points with studentized residuals greater than 3.000 or less

than −3.000).

2) High-leverage points (all points with leverage greater than 0.0171).

e. Using Cook’s Distance, examine the outliers and high-leverage points you found in

5d (if any) to determine if any are likely to be influential (Cook’s D > 1.000). If none

of the points appear to be influential, say so.

f. Conduct a formal hypothesis test at 𝛼𝛼 = 0.05 to determine if there is sufficient

evidence of a correlation between RBC and HBA1C. Include the following:

1) The p-value and its logical relationship to 𝛼𝛼 (≤ or >).

2) Your decision regarding the null hypothesis: reject or fail to reject.

3) A statement regarding the sufficiency of the evidence for a linear relationship

between RBC and HBA1C.

g. State whether the equation in 5a satisfies the following LINE criteria (assume the

residuals are independent):

Linear Relationship: Based on the model’s visual fit to the data, determine if a

linear model is appropriate.

Normally-Distributed Residuals: Determine if the residuals fit a normal distribution

using a residual histogram, a boxplot and a Q-Q plot.

Equal Variances of the Residuals: Assess the residuals for constant variance using a

plot of the residuals versus RBC.

h. Use the results from 5g and 5h to determine if the model you built in 5a provides

valid estimates of HBA1C as a function of RBC. Justify your decision.

i. Provide a valid point estimate of the mean HBA1C value when RBC = 20.000. Use

the regression model you constructed in 5a or calculate the estimate using the

HBA1C column by itself, whichever is appropriate.

j. Provide a valid 95% confidence interval estimate of the mean HBA1C value when

RBC = 20.000. Use the regression model you constructed in 5a or calculate the

estimate using HBA1C by itself, whichever is appropriate.

k. If you use the regression model from 5a to calculate the estimate in 5i, calculate a

95% prediction interval estimate of 𝑦𝑦𝑛𝑛𝑒𝑒𝑒𝑒, a new observation of HBA1C for a child aged 13. If the model in 5a is invalid, include a statement that a prediction interval

estimate is not applicable.

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