What is the formula for a confidence interval for a proportion?
\( \text{Confidence Interval} = \hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \)
What is the formula for the 10% condition?
n โค 10%N
What is the formula for the Large Counts Condition?
np โฅ 10 AND n(1-p) โฅ 10
What is the formula for calculating minimum sample size?
\( n = \left( \frac{z^*}{ME} \right)^2 \cdot p(1-p) \)
What is the formula for Point Estimate?
Sample proportion (pฬ)
Explain the concept of the Random Sample condition.
Reduces bias and allows results to be generalized to the larger population.
Explain the concept of the Independence condition.
Ensures that one subject's data doesn't influence another's, often checked using the 10% rule.
Explain the concept of the Normal condition.
Allows us to use the normal distribution (z-scores) for calculations; checked using the Large Counts condition.
Explain the impact of sample size on the margin of error.
Larger sample sizes lead to smaller standard errors, resulting in smaller margins of error and more precise estimates.
Explain the meaning of the confidence level.
The success rate of the method, not the probability of the interval containing the true parameter.
What is the definition of confidence interval?
A range of values, calculated from sample data, used to estimate a population parameter.
What is the definition of sample proportion?
Our best single guess for the population proportion, denoted as pฬ.
What is the definition of margin of error?
A buffer zone to account for uncertainty, added and subtracted from the point estimate.
What is the definition of critical value?
The z-score determined by the confidence level (e.g., 1.96 for 95%).
What is the definition of standard error of the proportion?
Variability of the sample proportion.
