A paper company sells paper that is supposed to* have a weight of 75.0 g/m2. In a quality inspection, the weights of 30 random samples of paper are measured. The sample mean of these weights is x- = 74.63 g/nr. with a sample standard deviation of s = 2.095 g/m2.
(a) Is there any evidence that the paper does not have an average weight of 75.0 g/m2?
(b) Construct a 99% two-sided t-interval for the average weight of the paper.
(c) If a 99% two-sided t-interval for the average weight of the paper is required with a length no longer than 1.5 g/m2, how many additional paper samples would you recommend need to be weighed?