Random Sampling and Reasoning

Choosing a sample in a way that everyone has an equal chance of being in the sample.

• Convenience Sampling

• Random Sampling

• Voluntary-Response Sampling

• Systematic Sampling

A movie theater randomly samples the types of admission tickets sold on Friday in the afternoon and the evening. If 400 tickets are sold on a Friday afternoon, use your inference and proportional reasoning skills to determine how many of those 400 tickets would be adult tickets. Type your numerical answer only.

A representative sample of 80 customers in a clothing store was surveyed about how they paid for their purchases. The table shows the responses. Based on the results, which of the following are valid inferences. Select all that apply.

• Tomorrow, 8 out of the first 80 customers will for sure pay with a gift card.

• In a group of 40 customers, it is expected that about 10 will pay with cash.

• About 0.3, or 30%, of all the store's customers will pay with a credit card.

• A sample of 100 customers would provide less reliable data.

Yadira wanted to estimate the mean number of words per page in a 180-page book she is reading. Which if these sampling methods gives the best estimate of the mean word count per page in the book?

• Count the words on one randomly chosen page.

• Calculate the mean word count for a sample consisting of the pages with pictures.

• Calculate the mean word count for a sample of 20 pages selected by choosing every 9th page.

• Calculate the mean word count for a sample consisting of the 10 pages that appear to have the most words.

Select all that apply!

• A

• B

• C

• D

• E

Which method would likely result in a random sample that is representative of the student population?

• Surveying all of the teachers at the school

• Surveying the students on the Student Council

• Surveying 100 students in the cafeteria at lunch

• Surveying 50 students who are in the school band.

Lana and Jeff each randomly surveyed 15 students about their favorite types of movies. What would you expect to see in the samples? Select all that apply.

• Different members are found in each sample.

• Some members may possibly overlap in each sample.

• Each sample gave the same responses.

• Both samples could be representative of the population.

• Both samples include only Lana and Jeff's friends.

Which method is most likely to produce a random sample of the members of your class?

• listing the first six students that come to mind

• choosing the five oldest students in the class

• writing the name of each student on a separate piece of paper and then drawing these slips from a hat

• selecting the first six students to arrive at class

A travel club has 3,000 members. A random sample of 50 of the club members found that 12 people like mountain vacations best. Which statement is NOT supported by the sample data?

• Twenty-four percent of those sampled say they like mountain vacations best.

• An estimated 720 club members would likely say they enjoy mountain vacations best.

• Almost one-quarter of club members would likely say they enjoy mountain vacations best.

• More than 2,500 club members would likely say they prefer other vacations over mountain vacations.

Using your inference skills and proportional reasoning, predict the number of purple jellybeans in a bag of 200 total jellybeans if a random sample of 25 resulted in 4 purple jellybeans. I predict there will be _________ purple jellybeans.