A random sample of 13 brands of caffeinated coffee resulted in the following 95% confidence interval for š, the average caffeine content in a cup of caffeinated coffee: (85.12, 154.08).Ā Interpret this interval.
Question
A random sample of 13 brands of caffeinated coffee resulted in the following 95% confidence interval for š, the average caffeine content in a cup of caffeinated coffee: (85.12, 154.08).Ā Interpret this interval.
Solution
This 95% confidence interval for the average caffeine content in a cup of caffeinated coffee means that we are 95% confident that the true average caffeine content for all brands of caffeinated coffee is between 85.12 and 154.08 milligrams. This is based on the sample of 13 brands that we tested. It's important to note that this doesn't guarantee that the true average is within this range, but it gives us a high degree of confidence. If we were to repeat this study many times, we would expect that 95% of the confidence intervals calculated from those studies would contain the true average.
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