The Accompanying Data Describe Flexural Strength (Mpa) for Concrete Beams

question 5

Multiple Choice

The accompanying data describe flexural strength (Mpa) for concrete beams of a certain type was introduced in Example 1.2. $$\begin{array} { l l l l l l l } 9.2 & 9.7 & 8.8 & 10.7 & 8.4 & 8.7 & 10.7 \\6.9 & 8.2 & 8.3 & 7.3 & 9.1 & 7.8 & 8.0 \\8.6 & 7.8 & 7.5 & 8.0 & 7.3 & 8.9 & 10.0 \\8.8 & 8.7 & 12.6 & 12.3 & 12.8 & 11.7 &\end{array}$$

• 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: \(\sum x _ { i } = 246.8 .\)
• 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.
• C) Calculate and interpret a point estimate of the population standard deviation \(\sigma\)
• Which estimator did you use? Hint: \(\sum x _ { i } ^ { 2 } = 2327.54\)
• D) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 11 Mpa. Hint: Think of an observation as a "success" if it exceeds 11.
• E) Calculate a point estimate of the population coefficient of variation \(\sigma / \mu\)
• And state which estimator you used.

---

Definitions:

Ethnographic-Based

Relating to or based on the systematic study of people and cultures from the perspective of the subject being studied.

Surveys

Research tools that collect data from a specific group of people using a series of questions to gather information on opinions, behaviors, or characteristics.

Focus Groups

A research method involving guided discussions among a small group of people to gather opinions on a particular subject.

Consumer Insights

Deep understandings about consumer behavior that inform marketing strategies and product development.