Question

A statistical program is recommended.

Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. An article reported data on ranges in maximum inclination angles of the head in the clockwise anterior, posterior, right, and left directions for 14 randomly selected subjects. Consider the accompanying data on average anterior maximum inclination angle (AMIA) both in the clockwise direction and in the counterclockwise direction.

Subj:	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Clockwise (Cl):	57.9	35.7	54.5	56.8	51.1	70.8	77.3	51.6	54.7	63.6	59.2	59.2	55.8	38.5
Counterclockwise (Co):	43.2	52.1	59.2	51.7	47.2	65.6	71.4	48.8	53.1	66.3	59.8	47.5	64.5	34.5

(a)Calculate a point estimate of the population correlation coefficient between Cl AMIA and Co AMIA

Cl = 786.7,

Co = 764.9,

Cl² = 45,727.31,

Co² = 43,166.87,

ClCo = 44,018.67. Round your answer to three decimal places.)

(b) Assuming bivariate normality (normal probability plots of the Cl and Co samples are reasonably straight), carry out a test at significance level 0.01 to decide whether there is a linear association between the two variables in the population (as do the authors of the cited paper).

H₀: ρ = 0
H_a: ρ ≠ 0

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t =____________

P-value =____________

Please answer a and b. Thanks

Answer 1

(a)Calculate a point estimate of the population correlation coefficient between Cl AMIA and Co AMIA

Ans : correlation coefficient between Cl AMIA and Co AMIA = 0.717

(b) Assuming bivariate normality (normal probability plots of the Cl and Co samples are reasonably straight), carry out a test at significance level 0.01 to decide whether there is a linear association between the two variables in the population (as do the authors of the cited paper).

H0: ρ = 0
Ha: ρ ≠ 0

Ans