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:
And the normal distribution.
Now we will substitute the values of the variables to finds the interval.
⇒ 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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