An article gave the following summary information for fracture strengths (mpa) of n = 174 ceramic bars fired in a particular kiln: x = 89.06, s = 3.22.

(a) calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. (give answers accurate to 1 decimal , )does it appear that true average fracture strength has been precisely estimated? yes, this is a very narrow interval. yes, this is a very wide interval. no, this is a very narrow interval. no, this is a very wide interval.

(b) suppose the investigators had believed a priori that the population standard deviation was about 5 mpa. based on this supposition, how large a sample would have been required to estimate μ to within .5 mpa with 95% confidence? (exact answer required.)n =