Title: How Hypothesis Tests Work: Confidence Intervals and Confidence Levels - Statistics By Jim
Headings: How Hypothesis Tests Work: Confidence Intervals and Confidence Levels
How Hypothesis Tests Work: Confidence Intervals and Confidence Levels
How to Interpret Confidence Intervals
Confidence Intervals Indicate the Precision of the Estimate
Creating Confidence Intervals Graphically
Confidence Intervals and the Inherent Uncertainty of Using Sample Data
Confidence Intervals and P Values Always Agree on Statistical Significance
Why They Always Agree
I Really Like Confidence Intervals!
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Content: For example, a 95% confidence level suggests that if you draw 20 random samples from the same population, you’d expect 19 of the confidence intervals to include the population value. The confidence interval procedure provides meaningful estimates because it produces ranges that usually contain the parameter. We’ll create a confidence interval for the population mean using the fuel cost example that we’ve been developing. With other types of data, you can create intervals for proportions, frequencies, regression coefficients, and differences between populations. Related post: See how confidence intervals compare to prediction intervals and tolerance intervals. Confidence Intervals Indicate the Precision of the Estimate
Confidence intervals include the point estimate for the sample with a margin of error around the point estimate. The point estimate is the most likely value of the parameter and equals the sample value. The margin of error accounts for the amount of doubt involved in estimating the population parameter. The more variability there is in the sample data, the less precise the estimate, which causes the margin of error to extend further out from the point estimate.