A normal population has the known mean 50 and unknown variance.
a) A random sample of n =16 is selected from this population, and sample results are = 52 and s=8. How strange are these results? Discuss.
b) A random sample of n =30 is selected from this population, and sample results are = 52 and s = 8. How strange are these results? Give details
c) A random sample of n=100 is selected from this population, and the sample results are = 52 and s = 8. How unusual are these results? Explain.
d) Compare your answers to parts (a)-(c) and explain why they are the same or differ.