In a sample of 80 ten-penny nails, the average weight was 1.56 g and the standard deviation was 0.1 g.
a. Find a 95% confidence interval for the mean weight of this type of nail.
b. Find a 98% confidence interval for the mean weight of this type of nail.
c. What is the confidence level of the interval (1.54, 1.58)?
d. How many nails must be sampled so that a 95% confidence interval specifies the mean to within ± 0.01 g?
e. Approximately how many nails must be sampled so that a 98% confidence interval will specify the mean to within ± 0.01 g?