Answer :
Final answer:
To find an 80% confidence interval for the population variance and standard deviation of automotive battery capacities, one uses the sample standard deviation and degrees of freedom in conjunction with a chi-square distribution table.
Explanation:
To construct an 80% confidence interval for the population variance and population standard deviation of the reserve capacities of automotive batteries, given a sample standard deviation of 0.25 hour from 18 samples, one can use the chi-square distribution.
To find the confidence interval for the population variance ($ ext ext ext ext ext), we need two chi-square values ($ ext ext ext ext ext) from the chi-square distribution table corresponding to the degrees of freedom ($ ext ext ext ext ext) which is n-1 (in this case, 17) and the desired confidence level (80%). The lower chi-square value corresponds to the higher percentile (60%) and the upper chi-square value corresponds to the lower percentile (20%), because of how the chi-square distribution is set up with respect to confidence intervals.
The formula to calculate the confidence interval for variance is given by:
CI for variance = $ ext ext ext ext ext
The formula for the standard deviation is just the square root of the variance, hence the CI for standard deviation can be obtained accordingly.