Chapter 6.1, Problem 1E

The accompanying data on flexural strength (MPa) for concrete beams of a certain type was introduced in Example 1.2.

1. a. Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion, and state which estimator you used. [Hint: Σx_i = 219.8.]
2. b. Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%, and state which estimator you used.
3. c. Calculate and interpret a point estimate of the population standard deviation σ. Which estimator did you use? [Hint: ${\displaystyle \sum x_i^2}\text{ = 1860}\text{.94}$.]
4. 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.]
5. e. Calculate a point estimate of the population coefficient of variation σ/μ, and state which estimator you used.