Question

Scores on the math SAT are normally distributed. A sample of 23 SAT scores had a standard deviation s=79. Construct a 95% confidence interval for the population standard deviation σ.

Answer 1

To construct a 95% confidence interval for the population standard deviation σ, use the chi-square distribution.

Step-by-step explanation:

To construct a 95% confidence interval for the population standard deviation σ, we can use the chi-square distribution. The chi-square distribution is used for estimating the population variance or standard deviation when the population follows a normal distribution.

To calculate the confidence interval, we need to find the upper and lower bounds using the chi-square distribution.

1. The upper bound is found by taking the square root of the chi-square value for the upper 2.5% of the distribution, multiplied by the sample variance divided by the critical value for chi-square at n-1 degrees of freedom.
2. The lower bound is found by taking the square root of the chi-square value for the lower 2.5% of the distribution, multiplied by the sample variance divided by the critical value for chi-square at n-1 degrees of freedom.

Once we have the upper and lower bounds, we can construct the 95% confidence interval for the population standard deviation σ.