A normal population has a known mean 50 and unknown variance.
(a) A random sample of n = 16 is selected from this population, and the sample results are x = 52 and s = 8. How unusual are these results? That is, what is the probability of observing a sample average as large as 52 (or larger) if the known, underlying mean is actually 50?
(b) A random sample of n = 30 is selected from this population, and the sample results are x = 52 and s = 8. How unusual are these results?
(c) A random sample of n = 100 is selected from this population, and the sample results are x = 52 and s = 8. How unusual are these results?
(d) Compare your answers to parts (a)–(c) and explain why they are the same or differ.