Can you make all of these statements about averages true at the same time?

Is the regularity shown in this encoded message noise or structure?

Get into the exponential distribution through an exploration of its pdf.

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

A random ramble for teachers through some resources that might add a little life to a statistics class.

Why MUST these statistical statements probably be at least a little bit wrong?

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

Can you decide whether these short statistical statements are always, sometimes or never true?