Confidence Interval introduction

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 used to estimate the uncertainty around a point estimate.

Front

What does the term 'point estimate' refer to?

Back

A point estimate is a single value given as an estimate of a population parameter. For example, the sample mean is a point estimate of the population mean.

Front

What is the margin of error in a confidence interval?

Back

The margin of error is the amount of error that is allowed in a statistical estimate. It defines the range above and below the point estimate.

Front

How do you calculate the margin of error?

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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 95% confidence).

Front

What does a 90% confidence interval indicate?

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A 90% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population parameter.

Front

If a confidence interval is (21, 45), what is the point estimate?

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The point estimate is the midpoint of the interval, which is (21 + 45) / 2 = 33.

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

Back

If a confidence interval does not contain a certain value, it suggests that the value is unlikely to be the true population parameter at the specified confidence level.

Front

True or False: Increasing the confidence level will decrease the width of the confidence interval.

Back

False. Increasing the confidence level will increase the width of the confidence interval.

Front

What is the relationship between sample size and confidence interval width?

Back

As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate.