Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 6.3 0.7 8.2 9.7 7.0 7.2 6.8 6.3 7.7 7.4 9.0 8.7 5.7 6.5 6.8 7.8 7.7 11.8 7.5 11.6 7.8 8.1 9.7 7.9 7.3 11.3 7.0 a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: ?xi = 219.5.] (Round your answer to three decimal places.) MPa State which estimator you used. x p? s / x s x tilde (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa State which estimator you used. s x p? x tilde s / x (c) Calculate a point estimate of the population standard deviation ?. [Hint: ?xi2 = 1857.11.] (Round your answer to three decimal places.) MPa Interpret this point estimate. This estimate describes the linearity of the data. This estimate describes the bias of the data. This estimate describes the spread of the data. This estimate describes the center of the data. Which estimator did you use? x tilde x s s / x p? (d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.) (e) Calculate a point estimate of the population coefficient of variation ?/?. (Round your answer to four decimal places.) State which estimator you used. p? x tilde s s / x x

Answer 1

a)

point estimate of the mean value =Σxi/n =				8.130
estimator to be used =x̅

b)

point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50% =median=											7.7
estimator to be used =x̃

c)

point estimate of the population standard deviation =sqrt((Σxi2-(Σxi)2/n)/(n-1))=								1.672
estimator to be used =s

This estimate describes the spread of the data

d)

point estimate of the proportion of all such beams whose flexural strength exceeds 10 Mpa=4/27=									0.1481
estimator to be used =p̂

e)

point estimate of the population coefficientof variation =						0.2056
estimator to be used =s/x̅