Inference Magnate Four Problems

1. You saw 3 inferential tests last week Large sample Z small sample t
Think of a measurable problem you know of and tell whether you would use a Z test or a t test 
Tell me why ( more than just being driven by sample size ) and describe the hoped for result 

2. Paired sample means tests are used when there is no historical data. 
Give me one example and some rationale where you would see a reason for wanting to use a paired sample means test 

3. A typical recommendation from an inferential test is to either not Reject the null implying no statistical difference in the means or to reject implying there is a statistical difference in the means. Usually the person giving the recommendation will include the confidence level ( aka the Alpha ) and will usually say "with a small chance of statistical error"
What is this statistical error and what do you think about this thing called error?

4. You just finished getting your data, made sure there were no fliers and the data was correct You created a mean and standard deviation and ran your Z test at the 0.05 alpha 
Your decision rule is 1.645 and your Z test statistic ( step 3 ) is 1.647 
What do you do ( reject or not ) and how do you feel about your decision