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Chapter 1: 1.1 (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 of certain 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

Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium; survival time for people in both groups was at most 6 hours. The accompanying data was read from a comparative boxplot in the article 鈥淔atal Excited Delirium Following Cocaine Use鈥� (J.

of Forensic Sciences, 1997: 25鈥�31).

ED0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3

.3 .4 .5 .7 .8 1.0 1.5 2.7 2.8

3.5 4.0 8.9 9.2 11.7 21.0

Non-ED0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2

.3 .3 .3 .4 .5 .5 .6 .8 .9 1.0

1.2 1.4 1.5 1.7 2.0 3.2 3.5 4.1

4.3 4.8 5.0 5.6 5.9 6.0 6.4 7.9

8.3 8.7 9.1 9.6 9.9 11.0 11.5

12.2 12.7 14.0 16.6 17.8

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Let \({\bar x_n}\) and \(s_n^2\) denote the sample mean and variance for the sample \({x_1},{x_2},...,{x_n}\) and let \({\bar x_{n + 1}}\) and \(s_{n + 1}^2\) denote these quantities when an additional observation \({x_{n + 1}}\) is added to the sample.

a. Show how\({\bar x_{n + 1}}\)can be computed from\({\bar x_n}\)and\({x_{n + 1}}\).

b. Show that

\(ns_{n + 1}^2 = \left( {n - 1} \right)s_n^2 + \frac{n}{{n + 1}}{\left( {{x_{n + 1}} - {{\bar x}_n}} \right)^2}\)

so that\(s_{n + 1}^2\)can be computed from\({x_{n + 1}}\),\({\bar x_n}\), and\(s_n^2\).

c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?

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\(\sum {\left| {{x_i} - \tilde x} \right|} /n = \left( {{{\bar x}_U} - {{\bar x}_L}} \right)/2\)

Then show that if n is odd and the two averages are calculated after excluding the median from each half, replacing non the left with n-1 gives the correct result.(Hint: Break the sum into two parts, the first involving observations less than or equal to the median and the second involving observations greater than or equal to the median.)

The actual tracking weight of a stereo cartridge that is set to track at \({\rm{3 g}}\) on a particular changer can be regarded as a continuous rv \({\rm{X}}\) with pdf

\({\rm{f(x) = \{ }}\begin{array}{*{20}{c}}{{\rm{k(1 - (x - 3}}{{\rm{)}}^2})}&{{\rm{2}} \le {\rm{x}} \le {\rm{4}}}\\{\rm{0}}&{{\rm{otherwise}}}\end{array}\)

a. Sketch the graph of \({\rm{f(x)}}\).

b. Find the value of \({\rm{k}}\).

c. What is the probability that the actual tracking weight is greater than the prescribed weight?

d. What is the probability that the actual weight is within \({\rm{.25 g}}\) of the prescribed weight?

e. What is the probability that the actual weight differs from the prescribed weight by more than \({\rm{.5 g}}\)?

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.?
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