Question

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

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

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.

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.

Part (a) Step 3: Explanation

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

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.

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.