The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)
How to find the confidence interval for standard deviation?
The formula for the confidence interval for the standard deviation is given by the formula;
CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
We are given;
Sample size; n = 19
D F = n - 1 = 19 - 1 = 18
Standard Deviation; s = 3.2
Confidence Level; CL = 95% = 0.95
Significance level; α = 1 - 0.95 = 0.05
Thus, using Chi-square distribution table online we have;
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
CI = √[(18 * 3.2²/(24.736)], √[(18 * 3.2²/(5.01)]
CI = (1.81, 4.03)
learn more about of Confidence Intervals here
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