Worksheet: Simple Random Sample

In this worksheet, we will practice choosing a simple random sample from a population.

Q1:

Which of the following choices would define a random experiment?

  • AIt is an experiment or a process for which the outcome can be predicted with certainty.
  • BIt is an experiment or a process for which the outcome cannot be predicted with certainty.

Q2:

Which of the following is an outcome of a random experiment?

  • Alanding the pointer of the spinner on the red color
  • Brolling a pair of dice
  • Cflipping a coin
  • Dchoosing two marbles from a jar
  • Edrawing a card from a pack of 52 cards

Q3:

The image shows a fair spinner.

Scarlett wants 5 random numbers from 1 to 5, so she spins the spinner 5 times. Her results are 3, 3, 5, 1, 3.

Which of the following statements about her results is true?

  • AThey are random numbers because the spinner is fair.
  • BThey are random numbers because their mean is the same as the mean of the numbers on the spinner.
  • CThey are not random numbers because there are too many threes.
  • DThey are not random numbers because there are no even numbers.

Q4:

Can simple random sampling be done with replacement?

  • AYes
  • BNo

Q5:

Suppose your school has 500 students and you need to conduct a short survey on the quality of the food served in the cafeteria. You decide that a sample of 10 students should be sufficient for your purposes.

Is that considered a simple random sample?

  • AYes
  • BNo

Q6:

An experiment consists in counting the number of heads when flipping a coin ten times. Is it a simple random experiment?

  • ANo
  • BYes

Q7:

An experiment consists of counting the number of boys in a family of three children. Does its output sample space correspond to an equiprobable random experiment?

  • AYes
  • BNo

Q8:

Imagine that you own a movie theater and you are planning a special horror-movie film festival next month. To decide which horror movies to show, you survey moviegoers, asking them which of the listed movies are their favorites. To create the list of movies needed for your survey, you decide to sample 100 of the 1,000 best horror movies of all time.

If you do that in a simple random sample, which of the following is true?

  • AThe probability of selecting the last 200 horror movies is lower than that of selecting the first 200.
  • BThe probability of selecting each horror movie is the same.
  • CThe probability of selecting the first 100 horror movies is greater than that of selecting the second 100.
  • DThe probability of selecting the last 100 horror movies is greater than that of selecting the first 100.
  • EThe probability of selecting the last 100 horror movies is lower than that of selecting the first 100.

Q9:

Which of the following is not a property of simple random sampling?

  • AAll the output has a probability of 2𝑛.
  • BAll possible samples of 𝑛 objects are equally likely to occur.
  • CThe population consists of 𝑁 objects.
  • DThe sample consists of 𝑛 objects.

Q10:

Imagine that you own a movie theater and you are planning a special horror-movie film festival next month. To decide which horror movies to show, you survey moviegoers asking them which of the listed movies are their favorites. To create the list of movies needed for your survey, you decide to sample 50 of the 1,000 best horror movies of all time.

What is the probability that a certain movie is selected (same for each horror movie)?

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