Samples, Surveys, and Drawing Inference

A researcher asked five of his doctor friends if they thought the new Brand X medicine that he developed was effective. Four responded "yes." The researcher used the results to write a TV advertisement claiming that "4 out of 5 doctors prefer Brand X medicine." Is this a valid inference? Explain.

• No, because the doctors asked are not a representative sample of the population of doctors.

• No, because 4 doctors said yes out of 9 who were asked.

• Yes, because the doctors asked are a representative sample of the population of doctors.

• Yes, because 4 doctors said yes out of the 5 who were asked.

Maria collects data from a random sample of 7th graders in her school and finds that 16 out of 20 7th graders participate in after-school activities. How many students should Maria expect to participate in after-school activities if 240 total 7th graders attend Maria's school? Write the numerical answer only.

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.

Trinity asked a random sample of 50 students at her school if they brought lunch from home today. If 30 answered “yes,” about what percent of students at Trinity’s school brought lunch from home today?

• 15%

• 30%

• 50%

• 60%

What inference can you draw from this survey?

• I can infer that most students in this school like pizza.

• I can infer that very few students like hamburgers.

• I can infer that their favorite is corn dogs.

• I can infer that most students in this school like hamburgers.

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.

True or False: all samples lead to a good prediction about an entire population.

• True

• False

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.

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.