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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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