Write a summary of the study and results. Be sure to present and discuss the nature Positive or negative and strength of the relationship between the two variables.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Assignment 10:

Instructions:  You must type your answers into an MS-Word (*.doc, *.docx, *.rtf, or PDF) file - you can use this file.  Be sure to correctly number each item.   You must submit (upload) your document to Assignment 10 (Assignment/Dropbox in BlackBoard.  Copy and paste the Scatter Plot into your document.  You must show the calculations (solutions) for all items marked with an asterisk (*) with on separate pages.    If you do not show your calculations/solutions, you will not receive credit for the assignment. Please report statistics to the correct number of decimal places (See questions).  You may not consult with anyone, except Dr. Napoli, for this assignment. 

Research Problem A: An investigator studying the relationship between diet and heart disease records the cholesterol levels of ten adult men during their annual medical exams.  The cholesterol measure (variable X) was scaled so that higher values reflect greater serum cholesterol levels.  Heart disease (variable Y) is measured as coronary stenosis – that is narrowing of the arteries expressed as percent diameter reduction in coronary arteries.   It is scaled so that higher (Y) values indicate more narrowing - also representing a greater risk for heart attack.  Test to see if cholesterol levels are related to coronary stenosis using the data below.  Set alpha = .01.

Question 1: fill in the table and compute the summary the statistic below the table (two decimal places)
Columns	a	b	c	d	e
	X	Y	XY	X2	Y2
	Cholesterol	% Arterial
Patient	Level	Narrowing
a	300	70
b	269	50
c	232	45
d	180	52
e	160	36
f	140	30
g	120	33
h	105	13
I	100	15
j	75	11
Sums
FILL IN THE SUMMARY STATISTICS BELOW
n =
ΣX =		ΣX2 =
ΣY =		ΣY2 =
ΣXY =

 Question 1:  Fill in columns c, d, e, the table above; and compute the Summary Statistic (n, ΣX, ΣX2, ΣY, ΣY2, ΣXY) to 2 decimal places.

Question 2: Write a Null and Alternative Hypothesis - Be sure that these hypotheses are specific to the problem (i.e., the relationship between cholesterol level and heart disease). 

Question 3: What are the  df & t critical value (both must be correct) 

Question 4:* Compute Pearson’s r  and r2 (to 3 decimal places) You must show the solutions to both).

Question 5:* Compute t = (to 2 decimal places) You must show the solution

Question 6: Do you reject or accept the Ho?  Explain why

Question 7: Write a summary of the study and results.   Be sure to present and discuss the nature (Positive or negative) and strength of the relationship (proportions of variation in Y explained by X) between the two variables. What can you conclude about the relationship between X and Y – that is do cholesterol levels have an impact on arterial narrowing?  If so, how?

Question 8:*  Compute the slope b = (to 3 decimal places) You must show the solution.

Question 9:*  Compute the intercept a = (to 3 decimal places)  You must show the solution.

Question 10:* If X = 250 what value would you estimate for Y’ = ? (2 decimal places). You must show the solution.

Question 11:* Compute the Standard Error of Estimate: Sest = ? (to 2 decimal places) You must show the solution. 

Question 12: Create a scatterplot for the X and Y variables.

Attachments:

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