Discuss the below:
Q: 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-bar = 52 and s= 8. How unusual are these results? Explain.
b) A random sample of n=30 is selected from this population and the sample results are x-bar = 52 and s=8. How unusual are these results. Explain.
c) A random sample of n=100 is selected from this population and the sample results are x-bar = 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