Respuesta :
Answer:
a) 95% confidence intervals are
(64.188, 72.652)
b) Mike use
(t₀.₀₂₅ , ₆)= 2.4469
Step-by-step explanation:
Step(i):-
Given data
x : 65 71 74 61 66 70 72
Mean of 'x'
x⁻ = ∑ x / n
[tex]x^{-} = \frac{65+71+74+61+66+70+72}{7} = 68.42[/tex]
x : 65 71 74 61 66 70 72
x - x⁻ : -3.42 2.58 5.58 -7.42 -2.42 1.58 3.58
(x-x⁻)² : 11.69 6.65 31.13 55.05 5.85 2.49 12.81
∑((x-x⁻)²) = 125.67
Variance
S² = ∑((x-x⁻)²) / n-1 = [tex]\frac{125.67}{6} = 20.945[/tex]
Standard deviation S = √20.945 =4.576
Step(ii):-
95% confidence intervals are determined by
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Degrees of freedom
ν =n-1 = 7-1 =6
[tex]t_{\frac{\alpha }{2} , n-1 } = t_{(\frac{0.05}{2} , 6)}[/tex] = (t₀.₀₂₅ , ₆)= 2.4469
[tex](68.42 - 2.4469 \frac{4.576}{\sqrt{7} } , 68.42 +2.4469\frac{4.576}{\sqrt{7} })[/tex]
( 68.42 - 4.232, 68.42 + 4.232)
(64.188, 72.652)
Conclusion:-
95% confidence intervals are
(64.188, 72.652)
