Subtopic 1:Now, without calculating a mean or margin of error or a confidence level, provide an example from your current (or your future) professional or personal life that describes a measurement that is normaland how much wiggle room on either side would be appropriate. When would you want a 95% confidence interval and when would you be interested in a 99% confidence level (a little more wiggle roomso a wider range)?

Subtopic 2: Two or more samples are often compared when we suspect that there are differences between the groupsfor example, are cancer rates higher in one town than another, or are test scores higher in one class than another? In your chosen field, when might you want to know the mean differences between two or more groups? Please describe the situation (what groups, what measurements) including how and why it would be used. Always keep in mind that statistics prove NOTHINGby itself. The statistical results MUST be supported by sound-science findings and real-world observations by credible persons. AND, even with 99% confidence levels (an alpha significance level of 1%), there is a 1% chance we are wrong in our conclusion.

For confidence intervals this conclusion would be that there is a 99% chance this CI, based on samples, contains the TRUE population mean. Or, for hypothesis tests, there is 99% confidence the null hypothesis (Ho) is accepted because the test statistic is NOT outside the range of the critical value (for that confidence level and sample size). This test statistic is calculated from sample statistics (mean, std dev) and a probability factor. So, what could go wrong?

• Type I error: We REJECT a TRUE null hypothesis ("false positive")
• Type II error: We ACCEPT a FALSE null hypothesis ("false negative")

Subtopic 3: Putting this in a real-world situation, in our legal system a defendant is presumed innocent until proven guilty. Ideally, the truly innocent will always go free, whereas the truly guilty will always be convicted. How has this worked out?

• What would be your ideal situation if you are the defendant?
• What would be your ideal situation if you are the prosecuting attorney?
• AND, As jurors, we must feel that the evidence presented justifies our decision (innocent or guilty) BEYOND a reasonable doubt. Is this ever possible, statistically speaking? Is there a ''more fair'' way?