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Chapter 1: Q9E (page 12)

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, 22, 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.Nonidenticalmeasurements are because of the errors such as recording error, measurement error etc.

b.The study is not enumerative.

Step by step solution

01

Given information

The number of observations Michelson and Newcomb obtained on the time it took for the light to travel between two locations is 66.

A few measurements that were coded in a certain manner are 31,23,32,36,22,26,27, and 31.

02

Explain the reason for nonidentical measurements.

a.

The provided measurements are nonidentical because ofcertain errorssuch as measurement error, changing of the environment when recoding the time, recoding error etc.

03

Check whether the study is enumerative.

b.

The study is said to beenumerativeif the population from which the sample is selected is finite and identifiable.

In the provided scenario, the population data is not provided. Therefore, it is not an enumerative study.

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Most popular questions from this chapter

One piece of PVC pipe is to be inserted inside another piece. The length of the first piece is normally distributed with mean value \({\rm{20}}\) in. and standard deviation \({\rm{.5}}\) in. The length of the second piece is a normal \({\rm{rv}}\)with mean and standard deviation \({\rm{15}}\) in. and \({\rm{.4}}\) in., respectively. The amount of overlap is normally distributed with mean value \({\rm{1}}\) in. and standard deviation \({\rm{.1}}\) in. Assuming that the lengths and amount of overlap are independent of one another, what is the probability that the total length after insertion is between \({\rm{34}}{\rm{.5 }}\) in. and \({\rm{35}}\) in.?

An experiment to study the lifetime (in hours) for acertain type of component involved putting ten components into operation and observing them for 100hours. Eight of the components failed during that

period, and those lifetimes were recorded. Denote the lifetimes of the two components still functioning after100 hours by 100+. The resulting sample observations were

48 79 100+ 35 92 86 57 100+ 17 29

Which of the measures of center discussed in this section can be calculated, and what are the values of those measures? (Note:The data from this experiment is said to be 鈥渃ensored on the right.鈥�)

The article cited in Exercise 20 also gave the following values of the variables y=number of culs-de-sac and z=number of intersections:

y

1

0

1

0

0

2

0

1

1

1

2

1

0

0

1

1

0

1

1

z

1

8

6

1

1

5

3

0

0

4

4

0

0

1

2

1

4

0

4

y

1

1

0

0

0

1

1

2

0

1

2

2

1

1

0

2

1

1

0

z

0

3

0

1

1

0

1

3

2

4

6

6

0

1

1

8

3

3

5

y

1

5

0

3

0

1

1

0

0

z

0

5

2

3

1

0

0

0

3

a. Construct a histogram for the ydata. What proportion of these subdivisions had no culs-de-sac? At least one cul-de-sac?

The article 鈥淢onte Carlo Simulation鈥擳ool for Better Understanding of LRFD鈥� (J. of Structural Engr., \({\rm{1993: 1586 - 1599}}\)) suggests that yield strength (\({\rm{ksi}}\)) for A36 grade steel is normally distributed with \({\rm{\mu = 43}}\) and \({\rm{\sigma = 4}}{\rm{.5 }}\)

a. What is the probability that yield strength is at most \({\rm{40}}\)? Greater than \({\rm{60}}\)?

b. What yield strength value separates the strongest \({\rm{75\% }}\) from the others?

The cdf for \({\rm{X( = measurement error)}}\) of Exercise \({\rm{3}}\) is

\({\rm{F(x) = }}\left\{ {\begin{array}{*{20}{c}}{\rm{0}}&{{\rm{x < - 2}}}\\{\frac{{\rm{1}}}{{\rm{2}}}{\rm{ + }}\frac{{\rm{3}}}{{{\rm{32}}}}\left( {{\rm{4x - }}\frac{{{{\rm{x}}^{\rm{3}}}}}{{\rm{3}}}} \right)}&{{\rm{ - 2}} \le {\rm{x < 2}}}\\{\rm{1}}&{{\rm{2}} \le {\rm{x}}}\end{array}} \right.\)

a. Compute \({\rm{P(X < 0)}}\).

b. Compute \({\rm{P( - 1 < X < 1)}}\).

c. Compute \({\rm{P(}}{\rm{.5 < X)}}\).

d. Verify that \({\rm{f(x)}}\) is as given in Exercise \({\rm{3}}\) by obtaining \({\rm{F'(x)}}\).

e. Verify that \(\widetilde {\rm{\mu }}{\rm{ = 0}}\).
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