The 95% confidence interval for the standard deviation of the height of the students is given by (1.541 – 4.059) .
Total number of students = 19 , hence n = 19
Standard deviation = 2.8 , hence s = 2.8
95% confidence interval, hence α = 1 - 0.95 = 0.05 .
Now the confidence interval is calculated using the formula:
![(\sqrt{\frac{(n-1)s^2}{\chi_{n-1,\alpha/2}^2}},\sqrt{\frac{(n-1)s^2}{\chi_{n-1,1-(\alpha/2)}^2}})](https://tex.z-dn.net/?f=%28%5Csqrt%7B%5Cfrac%7B%28n-1%29s%5E2%7D%7B%5Cchi_%7Bn-1%2C%5Calpha%2F2%7D%5E2%7D%7D%2C%5Csqrt%7B%5Cfrac%7B%28n-1%29s%5E2%7D%7B%5Cchi_%7Bn-1%2C1-%28%5Calpha%2F2%29%7D%5E2%7D%7D%29)
And the normal distribution.
Now we will substitute the values of the variables to finds the interval.
![(\sqrt{\frac{(19-1)2.8^2}{\chi_{19-1,0.05/2}^2}},\sqrt{\frac{(19-1)2.6^2}{\chi_{19-1,1-(0.05/2)}^2}})\\\\(\sqrt{\frac{94.64}{26.119}},\sqrt{\frac{94.64}{5.629}})](https://tex.z-dn.net/?f=%28%5Csqrt%7B%5Cfrac%7B%2819-1%292.8%5E2%7D%7B%5Cchi_%7B19-1%2C0.05%2F2%7D%5E2%7D%7D%2C%5Csqrt%7B%5Cfrac%7B%2819-1%292.6%5E2%7D%7B%5Cchi_%7B19-1%2C1-%280.05%2F2%29%7D%5E2%7D%7D%29%5C%5C%5C%5C%28%5Csqrt%7B%5Cfrac%7B94.64%7D%7B26.119%7D%7D%2C%5Csqrt%7B%5Cfrac%7B94.64%7D%7B5.629%7D%7D%29)
⇒ 1.541 – 4.059
Therefore the confidence interval is (1.541 – 4.059) .
A confidence interval is a collection of estimates for an unknown parameter (CI). However, other thresholds, like 90% or 99%, may also be used on occasion to produce confidence intervals. The most common confidence level has risen to be 95%.
The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. For instance, 95% of all intervals generated at the 95% confidence level should contain the parameter's real value.
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