Consider the accompanying data on flexural strength (MPa) for concrete beams of

Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

7.9 6.8 8.1 7.4 11.3 6.8 7.0

6.3 6.5 7.7 7.4 7.0 7.7 9.7

6.3 9.0 8.8 11.8 9.7 7.3 8.7

7.2 7.9 10.7 11.6 5.7 7.8

(a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: xi = 220.1.] (Round your answer to three decimal places.)

(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.

(c) Calculate a point estimate of the population standard deviation . [Hint: xi2 = 1867.39.] (Round your answer to three decimal places.)

(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.)

Explanation / Answer

1. We will use sample mean xbar to estimate popukation mean

xbar=sumxi/n=220.1/27=8.15185

2. We use sample median xbar=7.7, middle value when data arranged in ascending order.

3. We use the sample standard deviation sd=sqrt(sum(xi-mean)^2/(n-1))=sqrt(((sumxi^2)-(sum xi)^2/n))/(n-1))=1.6775

4. With success= observation greater than 10, we have success =4 and p=4/27=0.1481

5. We use sample sd/mean=1.6775/8.1519=0.2058

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