Question

You are still trying to estimate the girth of Kerrville toads. You collect 100 toads from many different ponds, rivers, witches cauldrons, etc around Kerrville. This is in the data set data("toad_girth") in my package. Using this data set find a 95% confidence interval for the population standard deviation of the toad girths:

Answer 1

Assumed values standard deviation values for the above data.
collect 100 toads from many different ponds, rivers, witches cauldrons, etc around Kerrville.
estimate the girth of Kerrville toads,95% confidence interval for the population standard deviation of the toad girths

CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ᴪ^2 right < σ^2 < (n-1) s^2 / ᴪ^2 left
where,
s = standard deviation
ᴪ^2 right = (1 - confidence level)/2
ᴪ^2 left = 1 - ᴪ^2 right
n = sample size
since alpha =0.05
ᴪ^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
ᴪ^2 left = 1 - ᴪ^2 right = 1 - 0.025 = 0.975
the two critical values ᴪ^2 left, ᴪ^2 right at 99 df are 128.422 , 73.361
s.d( s )=0.2771
sample size(n)=100
confidence interval for σ^2= [ 99 * 0.077/128.422 < σ^2 < 99 * 0.077/73.361 ]
= [ 7.602/128.422 < σ^2 < 7.602/73.361 ]
[ 0.059 < σ^2 < 0.104 ]
and confidence interval for σ = sqrt(lower) < σ < sqrt(upper)
= [ sqrt (0.059) < σ < sqrt(0.104), ]
= [ 0.243 < σ < 0.322 ]