Final answer:
To estimate the pass rate of California high school students on the exit exam with a 95% confidence level and 7% margin of error, approximately 196 student records must be sampled using a conservative estimate with a p-value of 0.5.
Step-by-step explanation:
In estimating the percentage of all California high school students who passed the high school exit exam on the first try with a 95% confidence level and a margin of error of 7%, you would use the formula for the sample size of a proportion:
n = (Z² × p × (1 - p)) / E²
Where:
- Z is the Z-score corresponding to a 95% confidence level, which is 1.96,
- p is the estimated proportion of students passing the exam (if unknown, 0.5 is used as it provides the maximum variance),
- E is the desired margin of error (0.07 in this case).
If no historical data is available to estimate 'p', the calculation with 'p' set to 0.5, which gives the largest required sample size, ensures a conservative estimate:
n = (1.96² × 0.5 × (1 - 0.5)) / 0.07²
n = (3.8416 × 0.25) / 0.0049
n = 0.9604 / 0.0049
n = 196.00
Therefore, you would need to sample approximately 196 student records to estimate the pass rate with the desired confidence and margin of error.