A simple random sample of size n is drawn from apopulation that is normally distributed. The sample mean, x, isfound to be 50, and the sample standard deviation, s, is found tobe 8.
a) Describe the sampling distribution of the sample meanx.
b) Construct a 98% confidence interval for μ if thesample size, n, is 20.
c) Construct a 98% confidence interval for μ if thesample size, n, is 15. How does decreasing the sample size affectthe margin of error, E?
d) Construct a 95% confidence interval for μ if thesample size, n, is 20. How does decreasing the level of confidenceaffect the margin of error, E?
e)If the population had not been normally distributedcould we have computed the confidence intervals in parts (b) –(d)?
