Final answer:
To construct the confidence interval for the population standard deviation, use the formula: Confidence Interval = ( s * sqrt(n - 1) / sqrt(chi-square(lower), chi-square(upper)) ). Substitute the given values and calculate the confidence interval. The confidence interval for the population standard deviation is ( 2.78, 10.73 ).
Step-by-step explanation:
To construct the confidence interval for the population standard deviation, we can use the formula:
Confidence Interval = ( s * sqrt(n - 1) / sqrt(chi-square(lower), chi-square(upper)) )
Where s is the sample standard deviation, n is the sample size, and chi-square(lower) and chi-square(upper) are the chi-square values corresponding to the desired confidence level.
For this question, the sample standard deviation is 7.1, the sample size is 17, and the desired confidence level is 0.8. We need to find the chi-square values corresponding to 0.1 and 0.9 percentiles for a sample size of 16 (df = n - 1).
Using a chi-square table or a chi-square calculator, we find that chi-square(0.1) = 7.563 and chi-square(0.9) = 27.587.
Now, we can substitute these values into the formula:
Confidence Interval = ( 7.1 * sqrt(17 - 1) / sqrt(7.563), 27.587 )
Calculating this, we get the confidence interval for the population standard deviation as ( 2.78, 10.73 ) rounded to one decimal place.