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: You can calculate a confidence interval from a sample to obtain a range for where the population parameter is likely to reside. For example, a confidence interval of [9 11] indicates that the population mean is likely to be between 9 and 11. Different random samples drawn from the same population are liable to produce slightly different intervals. If you draw many random samples and calculate a confidence interval for each sample, a specific proportion of the intervals contain the population parameter. That percentage is the confidence level. 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: