3. [5.01/6.68 Points]
DETAILS
PREVIOUS ANSWERS
DEVORESTAT9 7.SE.502.XP.
An article gave the following summary information for fracture strengths (MPa) of $n = 169$ ceramic bars fired in a particular kiln: $\bar{x} = 41.36$, $s = 3.94$.
(a) Calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. (Round your answers to two decimal places.)
$(40.7662, 41.9538)$ MPa
Does it appear that true average fracture strength has been precisely estimated?
Yes, 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 8 MPa. Based on this supposition, how large a sample would have been required to estimate $\mu$ to within 0.5 MPa with 95% confidence?
983 ceramic bars
You may need to use the appropriate table in the Appendix of Tables to answer this question.