Question 1

Which of the following best describes a simple random sample?

Accepted Answer

A sample where every possible sample of size $$n$$ has an equally likely chance of occurring.

Question 2

Sophia has six friends and wants to select three to attend a concert. If she uses simple random sampling, what is the probability that Michael, Kevin, and Marissa are chosen?

Accepted Answer

The probability is $$\frac{1}{20}$$, since there are $$\binom{6}{3} = 20$$ possible samples.

Question 3

Which of the following is NOT a requirement for a simple random sample?

Accepted Answer

Individuals can be selected more than once.

Question 4

If Sophia selects her friends by writing their names on slips of paper and drawing three slips from a hat, which sampling method is she using?

Accepted Answer

Simple random sampling

Question 5

How many possible simple random samples of size $$n = 3$$ can Sophia select from her six friends?

Accepted Answer

There are $$\binom{6}{3} = 20$$ possible samples.

Question 6

Which scenario below violates the principle of simple random sampling?

Accepted Answer

Sophia selects the first three friends who respond to her text.

Question 7

If Sophia wants to ensure that every possible group of three friends is equally likely to be chosen, which method should she use?

Accepted Answer

Simple random sampling

Question 8

Suppose Sophia selects three friends by picking every second name from an alphabetically ordered list. Is this a simple random sample?

Accepted Answer

No, because not every possible sample of size $$n is $$equally likely.

Question 9

In the context of simple random sampling, what does $$\binom{N}{n}$$ represent?

Accepted Answer

The number of possible samples of size $$n$$ from a population of size $$N.$$

Question 10

Sophia wants to select three friends from six, but she decides to always include Michael. How many possible samples are there now?

Accepted Answer

There are $$\binom{5}{2} = 10$$ possible samples.

Question 11

Which of the following statements is TRUE regarding simple random sampling?

Accepted Answer

It ensures that every possible sample of the specified size is equally likely.

Question 12

If Sophia selects three friends using simple random sampling, what is the probability that Annie is NOT selected?

Accepted Answer

The probability is $$\frac{\binom{5}{3}}{\binom{6}{3}} = \frac{10}{20} = 0.5$$

Question 13

Which of the following is a real-world example of simple random sampling?

Accepted Answer

A researcher randomly selects 100 names from a database of 10,000 patients using a random number generator.

Question 14

If Sophia wants to select three friends and uses a random number generator to assign numbers to each friend, which step ensures the sample is simple random?

Accepted Answer

Assigning numbers and randomly selecting three unique numbers.

Question 15

Why is it important that every possible sample of size $$n$$ has an equally likely chance of occurring in simple random sampling?

Accepted Answer

To ensure unbiased representation of the population.

Guided Practice: Simple Random Sampling and Sample Enumeration

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