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:

Conditioned Response

A response acquired through learning to a stimulus that was once neutral but has become associated with an unconditioned stimulus due to repeated pairings.

Surge of Excitement

An intense, sudden feeling of exhilaration or euphoria, often experienced in response to a stimulating event or anticipation of one.

Unconditioned Stimulus

In classical conditioning, an unconditioned stimulus is something that naturally and automatically triggers a response without any learning needed.

Conditioned Stimulus

A formerly neutral signal that, once linked with the unconditioned stimulus, ultimately induces a conditioned reaction.