Please answer the questions below based of the information I have provided below. Thank you so much for your help!

PART A:

1) Pick your variable x or y from the regression project.

2) Give a brief description as to why you chose this variable instead of the other.

3) Calculate the mean and standard deviation of your sample using statcrunch.

4) Compute the 95% Confidence Interval for the population mean using statcrunch.

5) Interpret what step 4 means.

PART B:

1) Use the same variable that was used for part A to come up with a claim. Make sure to explain your reasoning as to why to choose it.

2) Write both hypotheses

3) Tell about the tail of the test, find the test statistic and p value

4) Write the initial conclusion based on the p value approach using alpha = .05

5) Write the final conclusion using a complete sentence in reference to the context of your problem

6) Discuss the error (type 1 or 2) that would be associated with your decision

PART C:

1. Determine how many populations you will be comparing and set up the null and alternative hypothesis

2. Find the test statistic (F stat) and the P value

3. Use alpha = .05 to conclude whether the means are the same or different

Topic: Relationship between Body Mass Index (BMI) and Systolic Blood Pressure (SBP) in College Students.

The additional variable is the academic year.

Independent variable: Body Mass Index (BMI)

Dependent variable: Systolic Blood Pressure (SBP)

Expected finding: We expect to find a positive correlation between BMI and SBP.

This is because previous research has shown that a higher BMI is associated with higher blood pressure due to increased resistance in blood vessels.

Population: College students

Student #	BMI (kg/m^2)	SBP (mmHg)	Academic year	Major	Marriage Status
1	22.1	115	Freshman	Biology	Single
2	23.3	120	Freshman	Psychology	Single
3	25.4	126	Freshman	Computer Science	Single
4	27.8	135	Freshman	Economics	Single
5	24.9	129	Sophomore	Chemistry	Single
6	29.6	140	Sophomore	Education	Single
7	21.5	118	Sophomore	History	Married
8	25.8	128	Sophomore	Sociology	Single
9	26.2	132	Junior	Nursing	Single
10	28.4	137	Junior	English	Single
11	23.6	124	Junior	Physics	Single
12	22.9	117	Junior	Marketing	Married
13	27.3	131	Senior	Anthropology	Single
14	24.2	126	Senior	Music	Single
15	21.6	115	Senior	Political Science	Single
16	26.9	130	Senior	Art	Widowed
17	29.1	139	Senior	Mathematics	Single
18	25.3	123	Freshman	Psychology	Single
19	23.1	121	Freshman	Biology	Single
20	24.8	127	Freshman	Economics	Single
21	28.2	134	Sophomore	Chemistry	Single
22	22.8	119	Sophomore	Sociology	Single
23	26.7	133	Sophomore	Education	Single
24	30.1	142	Junior	Physics	Single
25	27.4	136	Junior	Marketing	Married
26	24.5	127	Junior	Nursing	Single
27	25.6	125	Senior	Political Science	Single
28	21.9	116	Senior	Anthropology	Single
29	23.8	122	Senior	Mathematics	Single
30	28.9	138	Senior	Music	Single

Solution 6

The correlation coefficient (r) is 0.9713. This indicates a strong positive linear relationship between BMI and SBP. As BMI increases, SBP tends to increase as well.

Solution 7

The coefficient of determination (r²) is 0.9432. This means that approximately 94.32% of the variation in SBP can be explained by variation in BMI. In other words, BMI is a very strong predictor of SBP.

Solution 8 -

Mean M_x: 25.4567,

Mean M_y: 127.5

Sum ofX= 763.7 Sum ofY= 3825 MeanX= 25.4567 MeanY= 127.5

X values(BMI)	Y Values (SBP)	X- Mx	Y- My	(X- Mx)2	(X- Mx)(Y- My)
22.1	115	-3.3567	-12.5	11.2672	41.9583
23.3	120	-2.1567	-7.5	4.6512	16.175
25.4	126	-0.0567	-1.5	0.0032	0.085
27.8	135	2.3433	7.5	5.4912	17.575
24.9	129	-0.5567	1.5	0.3099	-0.835
29.6	140	4.1433	12.5	17.1672	51.7917
21.5	118	-3.9567	-9.5	15.6552	37.5883
25.8	128	0.3433	0.5	0.1179	0.1717
26.2	132	0.7433	4.5	0.5525	3.345
28.4	137	2.9433	9.5	8.6632	27.9617
23.6	124	-1.8567	-3.5	3.4472	6.4983
22.9	117	-2.5567	-10.5	6.5365	26.845
27.3	131	1.8433	3.5	3.3979	6.4517
24.2	126	-1.2567	-1.5	1.5792	1.885
21.6	115	-3.8567	-12.5	14.8739	48.2083
26.9	130	1.4433	2.5	2.0832	3.6083
29.1	139	3.6433	11.5	13.2739	41.8983
25.3	123	-0.1567	-4.5	0.0245	0.705
23.1	121	-2.3567	-6.5	5.5539	15.3183
24.8	127	-0.6567	-0.5	0.4312	0.3283
28.2	134	2.7433	6.5	7.5259	17.8317
22.8	119	-2.6567	-8.5	7.0579	22.5817
26.7	133	1.2433	5.5	1.5459	6.8383
30.1	142	4.6433	14.5	21.5605	67.3283
27.4	136	1.9433	8.5	3.7765	16.5183
24.5	127	-0.9567	-0.5	0.9152	0.4783
25.6	125	0.1433	-2.5	0.0205	-0.3583
21.9	116	-3.5567	-11.5	12.6499	40.9017
23.8	122	-1.6567	-5.5	2.7445	9.1117
28.9	138	3.4433	10.5	11.8565	36.155
M: 25.4567	M: 127.5			SSx: 184.7337	SP: 564.95

Sum of squares (SS_X) = (X- M_x)²= 184.7337 Sum of products (SP) = (X- M_x)(Y- M_y) = 564.95 Regression Equation = =bX+a b=SP/SS_X= 564.95/184.73 = 3.05819 a= M_Y-bM_X= 127.5 - (3.06*25.46) = 49.64877 = 3.05819X+ 49.64877

Regression equation: = 3.05819X+ 49.64877

Let's say we want to predict the SBP for a person with a BMI of 26.7. We can plug in this value into the regression equation:

= 3.05819(26.7) + 49.64877

= 131.30244

Solution 8 (a)

The predicted SBP for a person with a BMI of 26.7 is 131.30244 mmHg.

The difference between the predicted y (131.30244) and the real y (133) would be the residual or error, which is:

e = y - e = 133 - 131.30244

e = 1.6975

The difference between the predicted y (131.30244 mmHg) and the real y (133 mmHg) is 1.6975 mmHg. This means that the prediction for the SBP of a person with a BMI of 26.7 is slightly lower than the actual SBP value that was observed. In other words, the model underestimated the SBP value for this particular individual. It's important to note that some degree of error is expected in any statistical model, and the goal is to minimize this error as much as possible.

Solution 8 (b)

Using the regression equation, we can make a prediction for the SBP of a person with a BMI of 27.5:

= 3.05819(27.5) + 49.64877

= 133.748995

The predicted SBP for a person with a BMI of 27.5 is 133.748995 mmHg.

Solution 8 (c)

The domain of the data is the range of values for the independent variable (BMI) that were included in the dataset. In this case, the domain is between the minimum value of BMI (21.5 kg/m^2) and the maximum value of BMI (30.1 kg/m^2) for the 30 students in the sample.

Solution 9

The Scatterplot with the line of best fit is given below -