An article gave the following summary information for fracture strengths (MPa) o

Question

An article gave the following summary information for fracture strengths (MPa) of n = 169 ceramic bars fired in a particular kiln: x-89.71, s-3.80 (a) Calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. (Give answers accurate to 1 decimal place.) 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 6 MPa. Based on this supposition, how large a sample would have been required to estimate to within .5 MPa with 95% confidence? (Exact answer required.)

Explanation / Answer

Z-value of 95 percent confidence interval is 1.96

CI = ( Mean+- Z* Standard deviation/sqrt(n) ) = (89.71- 1.96*3.8/13 , 89.71+ 1.96* 3.8/13) = (89.13,90.28) = (89.1,90.3)

Yes, because this is a very narrow interval.

c)

Standard error= 1.96* s/sqrt(n)

0.5 = 1.96*6/sqrt(n)

n= 553.19 or 554.

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