Inferences From Samples

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.

Johanna was running for class president. She wanted to know if she had a good chance of winning the election, so she decided to have her classmates help her with surveys. Michael surveyed a random sample of 10 students from the school. 7 of them said they would vote for Johanna. If there are 230 students in the school, and all of them vote, what is Michael’s best estimate of the number of students who would vote for Johanna? _________ students

Lucy collects data from a random sample of seventh-graders. Out of 40 respondents, 7 attend after-school programs. Of the 200 seventh-graders attending Lucy’s school, how many would be expected to attend afterschool programs?

Caleb is comparing the growth of plants using two different fertilizers. Use the measures of center from the box plots to make an inference about the data.

• Based on the means, plants in Group A grew more than plants in Group B

• Based on the means, plants in Group B grew more than plants in Group A.

• Based on the medians, plants in Group A grew more than plants in Group B

• Based on the medians, plants in Group B grew more than plants in Group A.

The dot plot shows a random sample of the number of fish caught and released by 30 participants during a two-day fishing derby.

Use the mean value of each data set to make an inference about the number of fish caught each day.

• On average, most participants caught and released 5 or more fish.

• More participants caught 6 fish than any other number.

• The same participants who caught and released 1 fish the first day caught and released 1 fish the second day.

• On average, participants caught and released more fish on Day 2.

Margo wants to convince her father to change her curfew from 9 P.M. to 10 P.M. She gathers data on curfew times from a random sample of students at her middle school. Can Margo use these data to present a valid inference that will convince her father? Explain.

• Yes; Most students have a curfew of 10 P.M. or later.

• Yes; More students have a curfew of 9 P.M. than any other time.

• No; Most students have a curfew of 9 P.M. or earlier.

• No; More students have a curfew of 10 P.M. or 11 P.M. than 8 P.M.

Russell randomly surveys seventh-graders in his school and finds that 6 of 30 attend summer camp. If there are 200 seventh-graders in his school, about how many are expected to attend summer camp? Enter your answer in the box.

Group A and Group B were randomly sampled from the same population. Select all the inferences that you can make.

• Group B has a higher median than Group A.

• Group B has a higher mean than Group A.

• Group B has more overall variability than Group A.

• Group B has a smaller range than Group A.

• Group A and B have the same maximum value.

If you compare the medians of each data set, who spends more time online?

• Seventh graders

• Eighth graders

• Both grades spend an equal amount of time online.

• Impossible to determine from the data sets.