Discuss the following problem:
Q: In an effort to estimate the annual income for new graduates, data were collected from 500 new graduates over a one -year period. assume a population standard deviation of $500.
a) if the sample mean is $15,000, what is the 95% confidence interval for the population mean?
b) if the sample mean is $15,000, what is the 98% confidence interval for the population mean?
c) discuss what happens to the width of the confidence interval as confidence level is increased. does this seem reasonable? explain.
d) if the data were collected for a sample of 25 rather than 500, develop a 95% confidence interval for the population mean (assuming the population has a normal probability distribution).
e) discuss what happens to the width of the confidence interval as the sample size decreases. Does this seem reasonable? explain.