Darchele wants to determine the color breakdown of color-coated chocolate candies in a bag of 500 candies. Which of the following simulations would help ensure that the sample is representative of the population?

A. Look through the bag to select 100 red candies.
Incorrect. A random sample is the most representative of the population, which in this case, is the entire bag of chocolate candies.

B. Count enough candies until 100 red candies are selected.
Incorrect. A random sample is the most representative of the population, which in this case, is the entire bag of chocolate candies.

C. Randomly select 100 candies from the bag, and count the colors.
Correct!

D. Sort the candies into each color, and count the number of colors.
Incorrect. A random sample is the most representative of the population, which in this case, is the entire bag of chocolate candies.

There are 150 patrons in the city library on a Saturday afternoon. Samantha, Bradley, and Addison each surveyed 20 randomly selected patrons to determine the types of media they preferred to use in the library. Which of the following statements best describes their survey results?

A. Their survey results are valid because each of them chose the same sample size.
Incorrect. A survey’s results are more likely to be valid if the sample is randomly selected. While sample size is important, random selection is more important.

B. Their survey results are not valid because they each surveyed 20 different patrons.
Incorrect. As long as the 20 patrons are selected randomly, each survey uses a different random sample from the population. Randomly selected samples from the same population are likely to generate similar valid results.

C. Their survey results are not valid because they were at the library on a Saturday afternoon instead of a Tuesday evening.
Incorrect. The day of the survey may influence the results because it helps define the population that is being surveyed. However, a random sample chosen from the population is likely to be representative of the population.

D. Their survey results are valid because they each chose a random sample from the same population, and a random sample is representative of the population.
Correct!

Micah wants to know what people in his community think about the city council’s plan to build a new park. He knows the ethnic and gender makeup of the community from recent census data, but does not have the resources to ask everyone in the community their opinion. Which of the following methods is most likely to generate accurate survey results?

A. Randomly select 50 people from the city’s telephone book to survey for their opinion.
Correct! A randomly selected sample is more likely to be representative of the population.

B. Visit a city park, and ask the first 50 people for their opinion.
Incorrect. The population being surveyed is the entire community, and people using an existing park may not represent the views of the entire community, which includes people who do not use the existing park. A randomly selected sample from the entire population is more likely to be representative of the population.

C. Select 50 people whose last name begins with the letter G to survey for their opinion.
Incorrect. A randomly selected sample is more likely to be representative of the population. Only using people whose last name begins with the letter G does not give every member of the population an equal chance of being selected for the sample.

D. At the local supermarket, ask the first 50 women who exit the supermarket for their opinion.
Incorrect. A randomly selected sample is more likely to be representative of the population. By restricting his survey to women, men are excluded from the survey. For a sample to be randomly selected, every member of the population must have an equal chance of being selected for the sample.

Sheree wants to select a random sample from a population of 250 students in the eighth grade class at her school. Which of the following simulations would most likely generate a representative sample?

A. Assign each student a number, and use a hundreds chart from her sister’s math book to select prime numbers.
Incorrect. Using a hundreds chart limits the survey to the first 100 students on the list, and there are 250 students in the population. 150 students have no chance of being selected for the sample.

B. Assign each student a number, and use a random number generator to select 50 numbers between 1 and 250.
Correct!

C. Use a bag of letter tiles to select a letter at random. Select all students whose last name begins with that letter for the sample.
Incorrect. While the letter is chosen at random, all students whose last name begins with the same letter may not be representative of the population.

D. Place 250 color tiles in a bag. Select 50 color tiles, and find 50 students whose shirt matches the color of the color tiles.
Incorrect. The color tile selection was random, but students’ selection of shirt colors may influence the outcomes possible in the sample, and the sample may not be representative of all eighth grade students.

Jacob knows that there are 225 seventh grade students in his middle school. He wants to determine which teacher is their favorite teacher, so he randomly selected 3 groups of 30 seventh grade students to determine which teacher is the favorite of seventh grade students. Which of the following best describes Jacob’s survey strategy?

A. The three groups should generate similar results, since a random sample is representative of the population from which it is selected.
Correct!

B. The three groups should generate different results, since each group was selected differently.
Incorrect. As long as each group was randomly selected, each group should yield similar survey results, since a random sample is representative of the population from which it is selected.

C. If Jacob had selected four groups instead of just three groups, his survey results would be more reliable.
Incorrect. A random sample is representative of the population from which it is selected. Increasing the number of samples does not necessarily increase the reliability of the survey results.

D. Jacob should select 30 students from both seventh and eighth grade, since most of the eighth grade students had the seventh grade teachers last year.
Incorrect. The population Jacob is studying is seventh grade students only, so including eighth grade students in the sample would make the samples not representative of the population of seventh grade students.