Respuesta :
95% confidence interval for true average degree of polymerization is [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.
Given :
- Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437, 438, 445, 447, 448, 453, 458, 462, 465 ]
- 95% confidence interval.
The total number of values given is, n = 17
Mean, μ₀ = 438.47
Standard Deviation, σ = 14.79
The normal distribution is given by: N (438.47 ; 14.79)
If Cl is 95% then is 5% and is 2.5%
α/2 = 0.025
Now, use t-statistics distribution with (n -1) degree of freedom
df = 16
So, the t score for 0.025 and 16 s from t-table 2.120.
CI = [ μ₀ ± [tex]t_{\alpha /2}[/tex] ; (n-1) × σ/ √n]
⇒ CI = [μ₀ ± 2.120 × 14.79/√17
⇒ CI = [ μ₀ ± 7.60]
⇒ CI = 430.87 ; 446.07]
Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.
No, the interval does not suggest that 451 is a plausible value.
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