Question

How the same data could be used for explaining confidence intervals for the difference in means and proportions. (Don’t forget to include what would be some differences in the analysis and interpretation.)

Answer 1

Solution:

Confidence levels are expressed as a percentage (for example, a 95% confidence level). It means that should you repeat an experiment or survey over and over again, 95% of experiments like we just did will include the true mean, but 5% won't.

So there is a 1-in-20 chance (5%) that our Confidence Interval does NOT include the true mean.

Say, that our 95% confidence interval for the average height in USA is 170m 10m or (160m - 180m). That means there is a 95% chance that the actual average height lies in this interval. Say we get to measure the height of all the people in USA (i.e we measure the true population mean) and we get an answer of 173m. Thus, the true mean does fall in our interval. But there is a 5% chance that the true mean does not, say the average mean = 181cm, and that's why we call it a 95% confidence. We have a 95% confidence that the mean falls in our interval.

Similarly, we can have a 90% , 99% confidence interval or any number for that matter.

We have a Z-score for a given confidence interval :

The formula for calculating the confidence interval is :

[ X ± (Z *s) /?n ]

Where:

• X is the mean
• Z is the chosen Z-value from the table above
• s is the standard deviation
• n is the number of samples