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 = 144 ceramic bars fired in a particular kiln: x = 75.80, s = 3.98. (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.) () 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 4 MPa. Based on this supposition, how large a sample would have been required to estimate mu to within 0.5 MPa with 95% confidence? ceramic bars

Explanation / Answer

a) Margin of error = (1.976692*3.98)/Sqrt(144) = 0.655603

95% Interval

(75.80-0.655603, 75.80+0.655603)

= (75.14, 76.46)

b) Sample size = (1.960*4/0.5)^2 = 246 (nearest integer)

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