Final answer:
The confidence intervals for the average breaking strength of wool fibers at different confidence levels are calculated, and it is observed that the interval widens as the confidence level increases. The value 450 is not plausible as the average breaking strength as it falls outside even the widest 99% confidence interval.
Step-by-step explanation:
To answer the student's question about constructing confidence intervals for the average breaking strength of wool fibers:
Part A: Constructing Confidence Intervals
The confidence interval can be constructed using the formula: CI = μ ± (z*(σ/√n)), where μ is the sample mean, σ is the sample standard deviation, n is the sample size, and z is the z-score corresponding to the confidence level.
For a 90% confidence interval, the z-score is approximately 1.645. For a 95% confidence interval, the z-score is approximately 1.96. For a 99% confidence interval, the z-score is approximately 2.576.
Plugging in the values (μ = 436.5, σ = 11.9, n = 20) into the formula for each confidence level, we get:
90% CI: (432.78, 440.22)
95% CI: (431.98, 441.02)
99% CI: (430.33, 442.67)
Part B: Comparing the Widths
The width of a confidence interval is determined by the z-score; higher confidence levels have wider intervals. Comparing the widths:
90% CI width: 440.22 - 432.78 = 7.44
95% CI width: 441.02 - 431.98 = 9.04
99% CI width: 442.67 - 430.33 = 12.34
The widest interval is at the 99% confidence level.
Part C: Plausibility of Average Breaking Strength
Given the 99% CI does not contain the value 450, it is not plausible that the average breaking strength is equal to 450 under the current evidence.