Answers
Answer:
Given That:-
As people age they begin experience hearing loss. A study was done on a random sample of 8 subsets to determine "confirmed" comfort level" of sound and again people.
| X | Y | X * Y | X2 | Ŷ | |
| 15 | 56 | 840 | 225 | 54 | |
| 25 | 57 | 1425 | 625 | 58.07143 | |
| 35 | 64 | 2240 | 1225 | 62.14286 | |
| 45 | 64 | 2880 | 2025 | 66.21429 | |
| 55 | 68 | 3740 | 3025 | 70.28571 | |
| 65 | 74 | 4810 | 4225 | 74.35714 | |
| 75 | 78 | 5850 | 5625 | 78.42857 | |
| 85 | 85 | 7225 | 7225 | 82.5 | |
| Total | 400 | 546 | 29010 | 24200 | 3631.049 |
(16) Assume the existence of a linear relationship between comfortable sound level and age, find the equation of the regresion line realting y to x.
Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2 )
b = ( 8 29010 - 400 546 ) / ( 8 * 24200 - ( 400 )2)
b = 0.4071
a =( ΣY - ( b * ΣX ) ) / n
a =( 546 - ( 0.4071 * 400 ) ) / 8
a = 47.8929
Equation of regression line becomes Ŷ = 47.8929 + 0.4071 X
(18) Find the predicted value of sound for a 60 year old person.
Ŷ = 47.8929 + 0.4071X
Ŷ = 47.8929 + 0.4071 (60)
Ŷ = 72.3189
(19) Construct a 90% prediction interval for the comfortable levle of sound for a 60 year ole person.
Estimated Error Variance 
S2 = ( 721.5 - 0.4071 * 1710 ) / 8 - 2
S2 = 4.2265
S = 2.0558
Predictive Confidence Interval of 
Ŷ = 47.8929 + 0.4071X
Ŷ = 72.3189
![1 se[yo] ta/2 x 1/[1+ - + n 20-0 SE](http://img.homeworklib.com/questions/824336a0-f8ee-11eb-9c68-31312a4a8ec1.png?x-oss-process=image/resize,w_560)
X̅ = (Xi / n ) = 400/8 = 50
![se yol = Y = 72.318972.3189 + 1.943 x 1 [1++ (60) - 50) 4200 -] x 4.2265 A](http://img.homeworklib.com/questions/8305ab40-f8ee-11eb-b514-f1e54ab5a302.png?x-oss-process=image/resize,w_560)
90% Predictive confidence interval is 
![ISSE SS 4 R = 0.9852 .- R502857 1710 21) jan(exy)-({x)(84) - [1823(53)?][654? czyjej • 8(2900) -(400) (546) f8f24200964023334](http://img.homeworklib.com/questions/83ddb7a0-f8ee-11eb-858b-4b8318914ac4.png?x-oss-process=image/resize,w_560)
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We were unable to transcribe this image
= 52 = (Sy – b * Szy)/n - 2
09=xlA
1 se[yo] ta/2 x 1/[1+ - + n 20-0 SE
t(4.2265/2) = t(0.1/2) = 1.943
se yol = Y = 72.318972.3189 + 1.943 x 1 [1++ (60) - 50) 4200 -] x 4.2265 A
(68.0375 < MY X=60 < 76.6003)
ISSE SS 4 R = 0.9852 .- R502857 1710 21) jan(exy)-({x)(84) - [1823(53)?][654? czyjej • 8(2900) -(400) (546) f8f242009640233343437989=654632 r=0.9823
.
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