Front

What is a 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

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

Back

A sample proportion is considered an unbiased estimator if the expected value of the sample proportion equals the true population proportion, meaning it does not systematically overestimate or underestimate the population parameter.

Front

How does sample size affect the sample proportion?

Back

As the sample size increases, the sample proportion is expected to be closer to the population proportion, reducing variability and increasing accuracy.

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 population parameter with a specified level of confidence (e.g., 95%).

Front

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

Back

A normal distribution allows for the application of statistical methods, such as confidence intervals and hypothesis testing, as many statistical techniques assume normality in the data.

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What is the formula for calculating a confidence interval for a population mean (μ)?

Back

The confidence interval for a population mean is calculated as: CI = x̄ ± z*(σ/√n), where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Front

What does a margin of error represent in polling?

Back

The margin of error indicates the range within which the true population parameter is expected to fall, given a certain level of confidence, reflecting the uncertainty in the estimate.

Front

How do you interpret a margin of error of 3% at a 95% confidence level?

Back

It means we are 95% confident that the true proportion of the population lies within 3 percentage points of the sample proportion.

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What is a point estimate?

Back

A point estimate is a single value estimate of a population parameter, such as the sample mean (x̄) for estimating the population mean (μ).

Front

What is the relationship between sample size and the standard error of the mean?

Back

The standard error of the mean decreases as the sample size increases, indicating that larger samples provide more precise estimates of the population mean.