A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a standard deviation equal to 6.4.
a. Find a 95% confidence interval for µ.
b. What do you mean when you say that a confidence coefficient is .95?
c. Find a 99% confidence interval for µ.
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?
e. Would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal? Explain.