Interval Estimation for Correlation Coefficients A two-sided 100%(1 – a) confidence interval for the population correlation coefficient (p) is : Lower limit: P1 Upper limit: P2 = ei#82+1 e221+1' where (z1,22) = z + (21-(a/2)/Vn – 3), and z = In We have a sample correlation coefficient ry based on a sample of n pairs of observations. Example: 95% CI for p when n = 10,r = 0.91 1. z=-In (1+ 0.91) In 1-0.91, 1.5275 (21,2) = 1.5275 + (1.96/V10 – 3) = ( 0.7867,2.2683) 2(0.7867 )-1 e2(0. 7867 )+1 e2(2.2683)-1 e2 (2.2063 )+1 1-1 Lower limit: P1 = = 0.6565; Upper limit: P2 0.9907. Thus, a 95% confidence interval for p = (0. 6565, 0. 9907). 1. A study was carried out into the attendance rate at a hospital of people in 16 different geographical areas, over a fixed period of time. The distance of the centre from the hospital of each area was measured in miles. The results were as follows: (1) 21%, 6.8; (2) 12%, 10.3; (3) 30%, 1.7; (4) 8%, 14.2; (5) 10%, 8.8; (6) 26%, 5.8; (7) 42%, 2.1; (8) 31%, 3.3; (9) 21%, 4.3; (10) 15%, 9.0; (11) 19%, 3.2; (12) 6%, 12.7; (13) 18%, 8.2; (14) 12%, 7.0; (15) 23%, 5.1; (16) 34%, 4.1. What is the correlation coefficient between the attendance rate and mean distance of the geographical area? Test its significance and find 95% confidence interval.
Interval Estimation for Correlation Coefficients A two-sided 100%(1 – a) confidence interval for the population correlation coefficient (p) is : Lower limit: P1 Upper limit: P2 = ei#82+1 e221+1' where (z1,22) = z + (21-(a/2)/Vn – 3), and z = In We have a sample correlation coefficient ry based on a sample of n pairs of observations. Example: 95% CI for p when n = 10,r = 0.91 1. z=-In (1+ 0.91) In 1-0.91, 1.5275 (21,2) = 1.5275 + (1.96/V10 – 3) = ( 0.7867,2.2683) 2(0.7867 )-1 e2(0. 7867 )+1 e2(2.2683)-1 e2 (2.2063 )+1 1-1 Lower limit: P1 = = 0.6565; Upper limit: P2 0.9907. Thus, a 95% confidence interval for p = (0. 6565, 0. 9907). 1. A study was carried out into the attendance rate at a hospital of people in 16 different geographical areas, over a fixed period of time. The distance of the centre from the hospital of each area was measured in miles. The results were as follows: (1) 21%, 6.8; (2) 12%, 10.3; (3) 30%, 1.7; (4) 8%, 14.2; (5) 10%, 8.8; (6) 26%, 5.8; (7) 42%, 2.1; (8) 31%, 3.3; (9) 21%, 4.3; (10) 15%, 9.0; (11) 19%, 3.2; (12) 6%, 12.7; (13) 18%, 8.2; (14) 12%, 7.0; (15) 23%, 5.1; (16) 34%, 4.1. What is the correlation coefficient between the attendance rate and mean distance of the geographical area? Test its significance and find 95% confidence interval.
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conclude that dosage and duration of relief are not correlated.
Interval Estimation for Correlation Coefficients
A two-sided 100%(1 – a) confidence interval for the population
correlation coefficient (p) is :
e2z1–1
Lower limit: P1 = 2221+1'
e2z2-1
Upper limit: P2 =
e2z2+1
where (z1,22) = z ± (z1-(a/2)/Vn – 3), and z =
We have a sample correlation coefficient rxy based on a sample of n
pairs of observations.
Example: 95% CI for p when n = 10,r = 0.91
(1+0.91'
= 1.5275
(160–1)m² - ()=-
(z,22) = 1.5275 + (1.96/V10 – 3) = ( 0.7867, 2.2683)
2(0.7867 )-1 - 0.6565;
e221-1
e21+1
e22-1
Upper limit: P2 = 222+1
Lower limit: p,
%3D
e2(0. 7867 )+1
e2(2.2683)-1
e2 (2.2863 )+1
= 0.9907.
Thus, a 95% confidence interval for p = (0. 6565, 0. 9907).
1. A study was carried out into the attendance rate at a hospital of people in 16
different geographical areas, over a fixed period of time. The distance of the centre
from the hospital of each area was measured in miles. The results were as follows:
(1) 21%, 6.8; (2) 12%, 10.3; (3) 30%, 1.7; (4) 8%, 14.2; (5) 10%, 8.8; (6) 26%, 5.8; (7)
42%, 2.1; (8) 31%, 3.3; (9) 21%, 4.3; (10) 15%, 9.0; (11) 19%, 3.2; (12) 6%, 12.7; (13)
18%, 8.2; (14) 12%, 7.0; (15) 23%, 5.1; (16) 34%, 4.1.
What is the correlation coefficient between the attendance rate and mean distance
of the geographical area? Test its significance and find 95% confidence interval.
Answer: ryy=(-) 0.848
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