Sampling and hypothesis testing

Is the age of this very old man statistically believable?

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

What information helped medical pioneers decide on the cause of a disease? Especially in a time before microscopes were as powerful as they are today ?

"Too much sleep is deadly" proclaimed the newspaper headline. Is this true?

How many trials should we do in order to accept or reject our null hypothesis?

Some short statements about hypothesis testing: are they true, false, or somewhere in between?

How effective are hypothesis tests at showing that our null hypothesis is wrong?