Margin of Error and Confidence Intervals

Front

What is the Margin of Error?

Back

The Margin of Error is a statistic that expresses the amount of random sampling error in a survey's results. It indicates the range within which the true population parameter is expected to fall.

Front

What is a Confidence Interval?

Back

A Confidence Interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. It is associated with a confidence level, such as 95%.

Front

What does a Z-score represent?

Back

A Z-score indicates how many standard deviations an element is from the mean. A positive Z-score means the value is above the mean, while a negative Z-score means it is below the mean.

Front

How do you calculate a Z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What Z-value corresponds to a 95% confidence interval?

Back

The Z-value for a 95% confidence interval is approximately 1.96.

Front

What is the purpose of using a Confidence Interval?

Back

The purpose of a Confidence Interval is to provide an estimated range of values that is likely to include an unknown population parameter, allowing for uncertainty in the estimate.

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 does it mean if a Confidence Interval is wide?

Back

A wide Confidence Interval indicates a high level of uncertainty about the estimate of the population parameter, often due to a small sample size or high variability in the data.

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Front

How do you interpret a 95% Confidence Interval of (1309.5, 2290.5)?

Back

It means that we are 95% confident that the true mean of the population lies between $1309.5 and $2290.5.