Question

Scores on the math SAT are normally distributed. A sample of 15 SAT scores had a standard deviation s=80. Construct a 95% confidence interval for the population standard deviation σ.

Answer 1

To construct a 95% confidence interval for the population standard deviation of SAT scores, use the chi-square distribution and the sample standard deviation.

Step-by-step explanation:

The student is asking how to construct a 95% confidence interval for the population standard deviation of SAT math scores given a sample standard deviation (s) of 80 with a sample size of 15 (n=15). To solve this, we will use the chi-square distribution and the following formula:

Confidence Interval for Population Standard Deviation: (sqrt((n-1)*s^2 / χ^2_{1-α/2}), sqrt((n-1)*s^2 / χ^2_{α/2}))

Where α is the significance level (0.05 for a 95% confidence interval), n is the sample size, s is the sample standard deviation, and χ^2 are the chi-square distribution critical values for degrees of freedom n-1.

For a sample size of 15:

1. Compute degrees of freedom: df = n - 1 = 15 - 1 = 14.
2. Find chi-square distribution critical values for df=14 and α/2 (0.025 and 0.975).
3. Plug these values into the confidence interval formula.