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 the sample proportion, this means that p̂ is expected to equal 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 variability.

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

How do you calculate a 95% confidence interval for a proportion?

Back

To calculate a 95% confidence interval for a proportion, use the formula: p̂ ± Z * sqrt[(p̂(1-p̂)/n)], where Z is the Z-score for 95% confidence (1.96), p̂ is the sample proportion, and n is the sample size.

Front

What is the significance of a normal distribution in estimating population parameters?

Back

A normal distribution allows for the use of standard statistical methods to estimate population parameters and calculate confidence intervals, especially when the sample size is large.

Front

What is the margin of error in statistics?

Back

The margin of error is the range within which the true population parameter is expected to fall, based on the sample estimate and the confidence level.

Front

What is the relationship between sample size and margin of error?

Back

As the sample size increases, the margin of error decreases, leading to a more precise estimate of the population parameter.

Front

What is the formula for determining the required sample size for estimating a proportion?

Back

The formula for sample size (n) is: n = (Z^2 * p̂(1-p̂)) / E^2, where Z is the Z-score, p̂ is the estimated proportion, and E is the desired margin of error.

Front

What does it mean if a sample is random?

Back

A random sample means that every individual in the population has an equal chance of being selected, which helps ensure that the sample is representative of the population.