Question 1

A finite population consists of five elements labeled A, B, C, D, and E. How many unique simple random samples of size 2 can be selected from this population?

Accepted Answer

$10$

Question 2

Given a population of five elements (A, B, C, D, E), which of the following is NOT a possible simple random sample of size 2?

Accepted Answer

$\{C, C\}$

Question 3

If you use simple random sampling to select a sample of size 2 from a population of 5 elements, what is the probability of selecting any specific sample?

Accepted Answer

$0.1$

Question 4

Suppose random number 1 corresponds to A, 2 to B, 3 to C, 4 to D, and 5 to E. Using the random digits 8 0 5 7 5 3 2, which pair is selected as a simple random sample of size 2?

Accepted Answer

$\{E, C\}$

Question 5

A finite population has 350 elements. Using the last three digits of the random number 98601, which element is selected for the sample?

Accepted Answer

$601$

Question 6

Given the random numbers 73022 and 83448, what are the last three digits used to select elements from a population of 350?

Accepted Answer

$022$ and $448$

Question 7

Why is it important to use the last three digits of a five-digit random number when selecting a sample from a population of 350 elements?

Accepted Answer

Because the last three digits ensure the selection is within the range $001$ to $350$

Question 8

If you are selecting a simple random sample of size 4 from a population of 350 using the random numbers 98601, 73022, 83448, and 02147, which elements are selected?

Accepted Answer

$601, 022, 448, 147$

Question 9

Which of the following best describes simple random sampling?

Accepted Answer

Every possible sample of the specified size has an equal chance of being selected

Question 10

If you select a sample of size 2 from a population of 5 elements, and you repeat the process 100 times, how many times would you expect to select the sample {A, B}?

Accepted Answer

$10$

Question 11

Which of the following is a key advantage of using random numbers in sampling?

Accepted Answer

It eliminates selection bias

Question 12

If you use the random numbers 34229 and 27553 to select elements from a population of 350, which elements are chosen?

Accepted Answer

$229$ and $553$ (ignore 553 as it exceeds 350)

Question 13

A researcher wants to select a simple random sample of size 2 from a population of 5. Which formula calculates the number of possible samples?

Accepted Answer

$C(n, k) = \frac{n!}{k!(n-k)!}$

Question 14

If a population has $N$ elements and you want to select a sample of size $n$, what is the probability of selecting any specific sample using simple random sampling?

Accepted Answer

$\frac{1}{C(N, n)}$

Sampling Methods and Simple Random Sampling in Statistics for Business

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