Math Problem Statement
An optical firm purchases glass for making lenses. Assume that the refractive index of 20 pieces
of glass have a variance of 1.2*10^-4
. Construct a 95% confidence interval for , the standard
deviation of the population samples.
Solution
To construct a 95% confidence interval for the standard deviation of the population, we will use the Chi-square distribution. The formula to calculate the confidence interval for the population standard deviation is:
Where:
- is the sample size (in this case, ),
- is the sample variance (given as ),
- is the significance level (for a 95% confidence interval, ),
- and are the critical values of the chi-square distribution with degrees of freedom.
Steps
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Math Problem Analysis
Mathematical Concepts
Statistics
Chi-square distribution
Confidence intervals
Variance and standard deviation
Formulas
Chi-square confidence interval for standard deviation formula: (sqrt((n-1) * s^2 / chi^2_alpha/2), sqrt((n-1) * s^2 / chi^2_1-alpha/2))
Theorems
Chi-square distribution theorem for variance and standard deviation estimation
Suitable Grade Level
Grades 11-12
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