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Chapter 1: Problem 9

In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were \(31,23,32,36,-2,26,27\), and 31 . a. Why are these measurements not identical? b. Is this an enumerative study? Why or why not?

Short Answer

Expert verified
a. They vary due to experimental error and measurement limitations. b. Yes, it's an enumerative study, as it describes specific observations without inference to a broader context.

Step by step solution

01

Understanding the Nature of Measurements

Michelson and Newcomb measured the time it took for light to travel between two points multiple times, resulting in slightly different results each time. This variability can be due to experimental error, environmental factors, and limitations in measurement precision.
02

Analysis of Non-Identical Measurements

No two trials are identical due to natural variability and random errors in observation and equipment. Factors like instrument accuracy, environmental conditions, and human error contribute to the variability in measurements.
03

Defining an Enumerative Study

An enumerative study aims to describe or summarize data from a specific set of observations or a finite population. It is concerned with historical or observed data without aiming to infer about other phenomena outside the observed data.
04

Evaluating if the Study is Enumerative

The described experiment is an enumerative study because it collects observations related to a specific event (the speed of light measurement) done a finite number of times, focusing solely on these measurements without generalizing to other contexts or times.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Experimental Error
In the world of probability and statistics, experimental error is an integral component to understand. When Michelson and Newcomb undertook their experiments on measuring light travel time, they likely encountered variations and discrepancies in their measurements.
This phenomenon is known as experimental error.
Experimental error stems from:
  • Inherent limitations in measuring devices: Instruments may have limits in precision, leading to slight variations in reading measured values.
  • Environmental factors: Changes in temperature, pressure, or other ambient conditions may affect measurements.
  • Human errors: Mistakes or inconsistencies by the person conducting the experiment, such as reading errors or timing inconsistencies.
By understanding these errors, researchers can design experiments that minimize their effects, leading to more reliable and valid results.
Enumerative Studies
When conducting an experiment like the one by Michelson and Newcomb, understanding the type of study is crucial. An enumerative study focuses on analyzing specific data collected from a particular set of observations.

In enumerative studies:
  • The focus is on describing or summarizing observed data.
  • The objective is not to infer or generalize beyond the study's data.
  • They use data from a finite population, or a specific example.
This characterized Michelson and Newcomb's work, as they were solely analyzing their collected observations on light travel time without attempting to draw conclusions about light outside of these readings.
Measurement Variability
Measurement variability is a common observation in experiments involving precise measurements, such as those of Michelson and Newcomb. It arises when multiple measurements are taken, revealing slight differences each time.

This variability can be attributed to several factors:
  • Random errors: Natural fluctuations that can cause measurements to differ slightly across repetitions.
  • Instrument precision: Variations depending on the accuracy of the measuring tools.
  • Environmental shifts: Changes in conditions that affect measurement stability.
Recognizing measurement variability is crucial as it allows scientists to quantify the reliability of their data.
Techniques like repeated measurements and statistical analysis help in identifying and correcting these variations, increasing the robustness of results.

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Most popular questions from this chapter

The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries \(4000,4200, \ldots\). [The histogram will agree with the one in "Comparison of Properties of Joints Prepared by Ultrasonic Welding and Other Means" (J. of Aircraft, 1983: 552-556).] Comment on its features. $$ \begin{array}{lllllll} 5434 & 4948 & 4521 & 4570 & 4990 & 5702 & 5241 \\ 5112 & 5015 & 4659 & 4806 & 4637 & 5670 & 4381 \\ 4820 & 5043 & 4886 & 4599 & 5288 & 5299 & 4848 \\ 5378 & 5260 & 5055 & 5828 & 5218 & 4859 & 4780 \\ 5027 & 5008 & 4609 & 4772 & 5133 & 5095 & 4618 \\ 4848 & 5089 & 5518 & 5333 & 5164 & 5342 & 5069 \\ 4755 & 4925 & 5001 & 4803 & 4951 & 5679 & 5256 \\ 5207 & 5621 & 4918 & 5138 & 4786 & 4500 & 5461 \\ 5049 & 4974 & 4592 & 4173 & 5296 & 4965 & 5170 \\ 4740 & 5173 & 4568 & 5653 & 5078 & 4900 & 4968 \\ 5248 & 5245 & 4723 & 5275 & 5419 & 5205 & 4452 \\ 5227 & 5555 & 5388 & 5498 & 4681 & 5076 & 4774 \\ 4931 & 4493 & 5309 & 5582 & 4308 & 4823 & 4417 \\ 5364 & 5640 & 5069 & 5188 & 5764 & 5273 & 5042 \\ 5189 & 4986 & & & & & \end{array} $$

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