Module 9 Practice Questions

Front

What is the formula to calculate the sample size needed to estimate a population proportion with a specified margin of error?

Back

n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score for the confidence level, p is the estimated proportion, and E is the margin of error.

Front

What does it mean for a sample proportion to be an unbiased estimator of the population proportion?

Back

It means that the expected value of the sample proportion equals the true population proportion, making it a reliable estimate.

Front

How does sample size affect the accuracy of the sample proportion as an estimator?

Back

Larger sample sizes lead to a sample proportion that is closer to the population proportion, reducing the margin of error.

Front

What is a confidence interval in the context of estimating a population proportion?

Back

A confidence interval is a range of values, derived from the sample data, that is likely to contain the true population proportion with a specified level of confidence.

Front

What is the significance of a 95% confidence level in statistical estimation?

Back

A 95% confidence level means that if we were to take many samples and build a confidence interval from each, approximately 95% of those intervals would contain the true population parameter.

Front

What is the Central Limit Theorem and how does it apply to sample proportions?

Back

The Central Limit Theorem states that the distribution of the sample proportion will be approximately normal if the sample size is large enough, regardless of the population distribution.

Front

What is the standard error of the sample proportion?

Back

The standard error of the sample proportion is calculated as SE = sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size.

Front

What is the role of random sampling in statistical estimation?

Back

Random sampling ensures that every individual has an equal chance of being selected, which helps to eliminate bias and makes the sample representative of the population.

Front

What does it mean if a sample size is considered 'large enough' for estimating proportions?

Back

A sample size is considered 'large enough' if both np and n(1-p) are greater than 5, ensuring the normal approximation is valid.

Front

How do you interpret a confidence interval of (0.42, 0.48) for a population proportion?

Back

This interval suggests that we are 95% confident that the true proportion of the population falls between 42% and 48%.