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Chapter 4: Q 16. (page 227)

Random digits Which of the following statements are true of a table of random digits, and which are false? Briefly explain your answers.

(a) There are exactly four 0s in each row of 40 digits.

(b) Each pair of digits has a chance 1/100 of being 00

(c) The digits 0000 can never appear as a group

because this pattern is not random.

Short Answer

Expert verified

Part (a) we would be able to tell if the 40 number was a 0 after looking at 39 digits, making it a predictable rather than random digit.

Part (b) the probability of each pair of digits is 1/100

Part (c) 0000 can appear as a group just as easily as any other string of four numbers.

Step by step solution

01

Part (a) Step 1: Given information

To choose random samples, we must explain why we should not always start at the same point in Table D.

02

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Part (a) Step 3: Explanation

Each row of 40numbers has exactly four 0sEach row of 40numbers has exactly four 0sThis assertion is false because if it were true, we would know if the 40number was a0 after looking at 39digits, and it would become a predictable rather than random digit.

04

Part (b) Step 1: Explanation

Each digit pair has a 1/10 chance of being 00

Each digit pair has a 1/10 chance of being 00 Because there are 100 pairings of digits from 00 to 99 all of them are equally likely, this assertion is "True." As a result, each pair of digits has a 1/100 chance of appearing.

05

Part (c) Step 1: Explanation

Because this pattern is not random, the numbers 0000 will never appear as a group. This statement is false because 0000 can appear as a group just as easily as any other string of four numbers.

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Most popular questions from this chapter

Dead trees On the west side of Rocky Mountain National Park, many mature pine trees are dying due to infestation by pine beetles. Scientists would like to

use sampling to estimate the proportion of all pine trees in the area that have been infected.

(a) Explain why it wouldn鈥檛 be practical for scientists to obtain an SRS in this setting.

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(c) Suppose that a more complicated random sampling plan is carried out, and that 35% of the pine trees in the sample are infested by the pine beetle. Can

scientists conclude that 35% of all the pine trees on the west side of the park are infested? Why or why not?

Sampling by accountants Accountants often use stratified samples during audits to verify a company鈥檚 records of such things as accounts receivable. The

stratification is based on the dollar amount of the item and often includes 100% sampling of the largest items. One company reports 5000 accounts receivable. Of these, 100 are in amounts over \(50,000;500 are in amounts between \)1000and\(50,000; and the remaining 4400are in amounts under \)1000Using these groups as strata, you decide to verify all the largest accounts and to sample 5% of the midsize accounts and 1%of the small accounts. How would you label the two strata from which you will sample? Use Table D, starting at line 115 to select only the first3 accounts from each of these strata.

an SRS of 5 students from your class to ask where they use a computer for the online exercises. You label the students 01,02,...,30 You enter the table

of random digits at this line:

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(a)14,45,92,60,56.(d)14,03,10,22,06.(b)14,31,03,10,22.(e)14,03,10,22,11.(c)14,03,10,22,22.

Cocoa and blood flowA study conducted by Norman Hollenberg, professor of medicine at Brigham and Women鈥檚 Hospital and Harvard Medical School,

involved 27healthy people aged 18-72. Each subject consumed a cocoa beverage containing 900milligrams of flavonols (a class of flavonoids) daily

for five days. Using a finger cuff, blood flow was measured on the first and fifth days of the study. After five days, researchers measured what they called 鈥渟ignifi-

cant improvement鈥� in blood flow and the function of the cells that line the blood vessels. What flaw in the design of this experiment makes it impossible to say

whether the cocoa really caused the improved blood flow? Explain.

Student archaeologists An archaeological dig turns up large numbers of pottery shards, broken stone tools, and other artifacts. Students working on the project classify each artifact and assign it a number. The counts in different categories are important for understanding the site, so the project director chooses 2% of the artifacts at random and checks the students鈥� work. Identify the population and the sample.
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