An article gave following summary information for fracture S

An article gave following summary information for fracture Strengths (MPa) of n = 144 ceramic bars fired m a particular in a particular kiln: x = 68.54, s = 3.81. Calculate a (two tided) 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. 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 born required to estimate mu to within 0.5 MPa with 95% confidence? ceramic bars You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

n =144, x bar =68.54, s = 3.81

std error = 3.81/rt 144 = 0.3175

Margin of error for 95% = 1.96(0.3175) = 0.6223

Confidence interval = (67.9177, 69.1623)

Yes, this is a narrow interval.

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Margin of error = 0.5 = 1.96(3.81/rtn)

Or rtn = 14.9352

Hence n should be atleast 223