Question

The mean and standard deviation measured from a randomly selected sample of n = 42 mathematics SAT test scores are x = 680 and s = 35. Find an approximate 99 percent confidence interval for the population mean μ.

Answer 1

To find an approximate 99 percent confidence interval for the population mean μ, use the formula CI = x ± Z * (s/√n), where x is the sample mean, Z is the z-score, s is the sample standard deviation, and n is the sample size. Substituting the given values, the confidence interval is (660.95, 699.05).

Step-by-step explanation:

To find an approximate 99 percent confidence interval for the population mean, we can use the formula:

CI = x ± Z * (s/√n)

where CI is the confidence interval, x is the sample mean, Z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.

Given that x = 680, s = 35, and n = 42, we need to find the z-score corresponding to a 99 percent confidence level. Consult a z-score table or use statistical software to find that the z-score is approximately 2.576.

Substituting the values into the formula:

CI = 680 ± 2.576 * (35/√42)

Simplifying the equation:

CI ≈ 680 ± 19.05

Therefore, the approximate 99 percent confidence interval for the population mean μ is (660.95, 699.05).