Question

Researchers want to know if there is a correlation between BMI and systolic blood pressure in males over 50. A random sample of 9 males is selected and their data is recorded below. a) Calculate the Pearson Correlation Coefficient for these two variables and b) test whether the correlation is significantly different from 0. Run the test at a 5% level of significance. Give each of the following for part b to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available. ID BMI Systolic blood pressure 1 18.5 122 2 20.0 112 3 22.3 120 4 25.4 136 5 26.9 140 6 28.7 117 7 30.4 152 8 32.7 165 9 33.4 162

Answer 1

Answer:

Given that  correlation between BMI and systolic blood pressure in males over 50.

Sr.	BMI(X)	Sys Bl Pr (Y)
1	18.5	122	-7.98	-14.22	63.64	202.27	113.46
2	20	112	-6.48	-24.22	41.96	586.72	156.71
3	22.3	120	-4.18	-16.22	17.45	263.16	67.77
4	25.4	136	-1.08	-0.22	1.16	0.05	0.24
5	26.9	140	0.42	3.78	0.18	14.27	.60
6	28.7	117	2.22	-19.22	4.94	369.49	-42.72
7	30.4	152	3.92	15.78	15.38	248.94	61.88
8	32.7	165	6.22	28.78	38.72	828.16	179.06
9	33.4	162	6.92	25.78	47.92	664.49	178.44
Total	238.3	1226	0.00	0.00	231.36	3177.56	716.64
Mean=	26.478	136.222

(a) Correlation coefficient (r)

We can say that there is strong positive correlation.

(b) Test:

is the population correlation coefficient

(1)

H₀: = 0 (There is no linear relation between BMI and systolic blood pressure.)

VS

H_1: (There is linear relation between BMI and systolic blood pressure.)

2)

we are going to use t-test for the correlation coefficient test with 'n-2' degrees of freedom.

3) I am using the p-value method approach.

Decision rule: Reject null hypothesis if p-value<0.05 (level of significance)

(4) Test statistic=

Test Stat = 4.0281

p-value is the probability of null hypothesis being true

(5) p-value = P(t_n-2 > T.S)

=P(t₇>4.0281)

P-value = 0.0025 found using t-dist tables where df =7 and x=4.0281

(5) Since p-value<0.05

Decision: We reject the null hypothesis at 5% level of significance.

Conclusion: We conclude that there is a significant linear relation between BMI and systollc blood pressure.

(a)Correlation coefficient (r) = Σα-1ν- ΜΣ- Σ ν-J

716.64 231.36 * 3177.56

r = 0,836

We can say that there is strong positive correlation.

(b) Test

is the population correlation coefficient

(1)

Но : р— 0 (There is no linear relation between BMI and systolic blood pressure.)

VS

H_{1}:\ 0 (There is a linear relation between BMI and systolic blood pressure.)

2)

We are going to use a t-test for the correlation coefficient test with 'n-2' degrees of freedom.

(3) I am using the p-value method approach.

Decision rule: Reject null hypothesis if p-value < 0.05 (level of significance)

(4)Test statistic = ryn – 2 V1 - r2

=

p-value is the probability of null hypothesis being true

(5) p-value = P (t_{n-2} > T.S.)

= P (t_{7} > 4.0281)

{p-value=0.0025}found using t-dist tables where df = 7 and x = 4.0281

(5) Since p-value < 0.05

Decision: We reject the null hypothesis at 5% level of significance.

Conclusion: We conclude that there is a significant linear relation between BMI and Systolic blood pressure.

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