Final answer:
A 95% confidence interval for the population standard deviation σ can be constructed using the sample standard deviation (78), sample size (17), and the chi-square distribution. The values required from the chi-square table allow for the calculation of the interval.
Step-by-step explanation:
To construct a 95% confidence interval for the population standard deviation σ, when the sample standard deviation (s) is known, and the data is normally distributed, we use the chi-square (χ2) distribution formula. The formula for the confidence interval for σ is:
σ = s ∙ √(n - 1) / χ2α/2, σ = s ∙ √(n - 1) / χ21-α/2
Where:
• s is the sample standard deviation (78)
• n is the sample size (17)
• α is the level of significance (0.05 for 95% confidence)
• χ2α/2 and χ21-α/2 are the chi-square values for α/2 and 1-α/2 degrees of freedom respectively.
Using a chi-square table or calculator, the values of χ2α/2 and χ21-α/2 can be obtained, and then the confidence interval can be calculated accordingly.