Question

the following represents the PH of rain for a random sample of 12 rain dates in a particular region. A normal probability distribution plot suggest that the data could come from a population that is normally distributed. a boxplot indicates there are no outliers. The sample standard deviation s=0.326. construct and inerprete a 99% confidence interval for the standard deviation PH of rain water in this region

Answer 1

Given

n = 12 , s = 0.326

The 99% confidence interval for the standard deviation PH of rain water in this region is

(n-1)*s^{​​​​​​2}​​​​​/²_a/2 < < (n-1)*s^{​​​​​​2}/²1-a_/2

For a = 0.01 , d.f = n -1 = 11

  ²_{/2 , n-1} = ²_{0.001 , 11} = 26.757

  ²​​​​​​_{1-a/2 , n-1} = ²_{0.995, 11} = 2.603

Sqrt[11*0.326²/26.757] < < sqrt [11*0.326²/2.603]

0.209 < < 0.670

we are 99% confident that the true standard deviation PH of rain water in this region lies between 0.209 to 0.670