Mathematics: Evaluate : (i) −5 8 7 3 (ii) −6 −11 X (-4)

Step-by-step explanation:Given : Confidence level :Significance level :Sample size : n= 16Sample standard deviation : s= 3.6 inchesUsing chi-square distribution table , the critical values are:We know that , confidence interval for the population standard deviation is given by :- Hence , a 99% confidence interval for the population standard deviation is ....

Evaluate : (i) −5 8 7 3 (ii) −6 −11 X (-4)

Ответ:

mluz

03.09.2022

Mathematics

$2.43<\sigma<6.50$

Step-by-step explanation:

Given : Confidence level : $1-\alpha=0.99$

Significance level : $\alpha=0.01$

Sample size : n= 16

Sample standard deviation : s= 3.6 inches

Using chi-square distribution table , the critical values are:

$\chi^2_{\alpha/2, n-1}=\chi^2_{0.005, 15}=32.80132065\\\\\chi^2_{1-\alpha/2, n-1}=\chi^2_{0.995, 15}=4.60091557$

We know that , confidence interval for the population standard deviation is given by :-

$\sqrt{\dfrac{(n-1)s^2}{\chi^2_{\alpha/2, n-1}}}<\sigma<\sqrt{\dfrac{(n-1)s^2}{\chi^2_{1-\alpha/2, n-1}}}\\\\=\sqrt{\dfrac{(15)(3.6)^2}{32.80132065}}<\sigma<\sqrt{ \dfrac{(15)(3.6)^2}{4.60091557}}\\\\= 2.43445900391<\sigma< 6.50018920988\\\\\approx2.43<\sigma<6.50$

Hence , a 99% confidence interval for the population standard deviation is $2.43<\sigma<6.50$ .

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