## 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

X̅ = (Xi / n ) = 400/8 = 50

90% Predictive confidence interval is

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