Module 9 Practice Questions

Front

What is the sample proportion (p̂) in statistics?

Back

The sample proportion (p̂) is the ratio of the number of successes in a sample to the total number of observations in that sample, used as an estimator for the population proportion (p).

Front

What does it mean for an estimator to be unbiased?

Back

An estimator is unbiased if its expected value equals the true value of the parameter being estimated. For example, the sample proportion p̂ is an unbiased estimator of the population proportion p.

Front

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

Back

As the sample size increases, the sample proportion (p̂) is expected to be closer to the population proportion (p), reducing the margin of error.

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from a sample, that is likely to contain the true population parameter with a specified level of confidence (e.g., 95%).

Front

What is the formula for calculating the sample size needed for estimating a proportion?

Back

The formula is n = (Z^2 * p̂ * (1 - p̂)) / E^2, where Z is the Z-score corresponding to the desired confidence level, p̂ is the estimated proportion, and E is the margin of error.

Front

What is the significance of a normal distribution in statistics?

Back

A normal distribution is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean.

Front

What does a 95% confidence level indicate?

Back

A 95% confidence level indicates that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population parameter.

Front

What is the margin of error in the context of confidence intervals?

Back

The margin of error is the range of values above and below the sample statistic in a confidence interval, indicating the precision of the estimate.

Front

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

Back

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

Front

What is the role of random sampling in statistics?

Back

Random sampling ensures that every individual has an equal chance of being selected, which helps to eliminate bias and allows for generalization of results to the larger population.