Unit 8A Practice Confidence Intervals

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence.

Front

What does a 95% confidence interval mean?

Back

A 95% confidence interval means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population parameter.

Front

How do you calculate the margin of error for a proportion?

Back

Margin of error = Z * sqrt[(p(1-p)/n)], where Z is the Z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

Front

What is the formula for a confidence interval for a population proportion?

Back

Confidence interval = p ± Margin of error.

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What is the standard deviation in the context of a normal distribution?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

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What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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What does it mean if a confidence interval does not contain a certain value?

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If a confidence interval does not contain a certain value, it suggests that the value is not a plausible estimate of the population parameter.

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What is a point estimate?

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A point estimate is a single value estimate of a population parameter, such as the sample mean or sample proportion.

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How do you interpret a confidence interval of (0.316, 0.384)?

Back

This interval suggests that we are 95% confident that the true proportion of women Internet users in Europe lies between 31.6% and 38.4%.

Front

What is the significance of the sample size in confidence intervals?

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A larger sample size generally results in a smaller margin of error and a more precise confidence interval.