Question

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level in an earlier study, the population proportion was estimated to be 0.23. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99% confidence level with an error of at most 0.02? Round your answer up to the next integer.

Answer 1

To estimate the required sample size to estimate the fraction of tenth-graders reading at or below the eighth-grade level, we can use the formula for sample size calculation for proportions. Using a 99% confidence level and an error of at most 0.02, the required sample size would be 693 students.

Step-by-step explanation:

To estimate the required sample size, we need to use the formula for sample size calculation for proportions. The formula is:

sample size = (Z^2 * p * (1-p)) / E^2

where:

• Z is the z-score corresponding to the desired confidence level (99% confidence level corresponds to a z-score of approximately 2.576)
• p is the estimated population proportion of 0.23
• E is the maximum error or margin of error of 0.02

Using these values, substitute them into the formula and solve for sample size:

sample size = (2.576^2 * 0.23 * (1-0.23)) / 0.02^2 = 692.81

Rounding up to the next integer, the required sample size would be 693.