Module 9 Practice Questions (2)

Front

What is the sample proportion (p̂)?

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

Is the sample proportion (p̂) always equal to the population proportion (p)?

Back

No, the sample proportion can vary from sample to sample and is not always equal to the population proportion.

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, it is an unbiased estimator of the population proportion.

Front

How does sample size affect the sample proportion (p̂)?

Back

The larger the sample size, the closer the sample proportion is expected to be to the population proportion, 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.

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 for the desired confidence level, p̂ is the estimated proportion, and E is the margin of error.

Front

What is the significance of a 95% confidence level?

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 proportion.

Front

What is the margin of error in the context of estimating proportions?

Back

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

Front

What does it mean if a variable has a normal distribution?

Back

A variable has a normal distribution if its values are symmetrically distributed around the mean, forming a bell-shaped curve.

Front

What is the role of random sampling in statistical estimation?

Back

Random sampling ensures that every individual in the population has an equal chance of being selected, which helps to reduce bias and improve the validity of the results.