Mathematics: Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation sigma. assume that the population has a normal distribution. round the confidence interval limits to the same number of decimal places as the sample standard deviation. the mean replacement time for a random sample of 20 washing machines is 11.6 years and the standard deviation is 2.8 years. construct a 99% confidence interval for the standard deviation, sigma, of the replacement

Decreasing then increasing always increasing...

Use the given degree of confidence and sample data

Karolina0304

16.03.2022

1.97

Step-by-step explanation:

The confidence interval for population standard deviation is given by :-

$s\sqrt{\dfrac{(n-1)}{\chi^2_{n-1,\alpha/2}}}$

Given : Sample size : n=20

Standard deviation : $s=2.8\text{ years}$

Significance level : $\alpha: 1-0.99=0.01$

Critical value using chi-square distribution table :

$\chi^2_{n-1,\alpha/2}=\chi^2_{19,0.005}=38.58$

$\chi^2_{n-1,1-\alpha/2}=\chi^2_{19,0.995}=6.84$

Then , 99% confidence interval for the standard deviation of the replacement times of all washing machines of this type will be :

$2.8\sqrt{\dfrac{(19)}{38.58}}$

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