1.8 MOE & Confidence Intervals

Front

What is the definition of 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 used to estimate the uncertainty around a sample statistic.

Front

What does the margin of error represent in statistics?

Back

The margin of error is a measure of the uncertainty or potential error in a survey's results. It indicates the range within which the true population parameter is expected to fall.

Front

How do you calculate the margin of error?

Back

The margin of error can be calculated using the formula: Margin of Error = Critical Value × Standard Error.

Front

What is the critical value in the context of confidence intervals?

Back

The critical value is a factor used to compute the margin of error, which corresponds to the desired confidence level (e.g., 1.96 for a 95% confidence level).

Front

If the mean of a sample is 21 and the margin of error is 5.1, what is the confidence interval?

Back

The confidence interval is (21 - 5.1, 21 + 5.1) = (15.9, 26.1).

Front

Given a confidence interval of 19 to 33, how do you find the margin of error?

Back

The margin of error is calculated as (Upper Limit - Lower Limit) / 2. For this interval, it is (33 - 19) / 2 = 7.

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

If the mean of a survey is 84 and the margin of error is 3.7, what are the reasonable values for the population?

Back

The reasonable values for the population are from (84 - 3.7) to (84 + 3.7), which is (80.3, 87.7).

Front

What does it mean if a value is outside the confidence interval?

Back

If a value is outside the confidence interval, it suggests that the value is not a plausible estimate of the population parameter based on the sample data.

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How do you determine if a value is NOT reasonable given a mean and margin of error?

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A value is NOT reasonable if it falls outside the range defined by (mean - margin of error) to (mean + margin of error).