# Estimating Population Proportions

Warmup

A teacher asked all the students in one class how many minutes it takes them to get to school. Here is a list of their responses:

(2.) What fraction of the students in this class say it takes them more than 10 minutes to get to school?

(3.) If the whole school has 720 students, can you use this data to estimate how many of them would say that it takes them more than 10 minutes to get to school? Be prepared to explain your reasoning.

Activity #1

`Practice Exercise Questions on Population Proportions.`

• Use the survey data below to answer the questions that follow.

Here are the results of a survey of 20 people who read The Adventures of Super Sam regarding what special ability they think the new hero should have.

(1.) What proportion of this sample want the new hero to have the ability to fly?

(2.) If there are 2,024 dedicated readers of The Adventures of Super Sam, estimate the number of readers who want the new hero to fly.

Two other comic books did a similar survey of their readers.

• In a survey of people who read Beyond Human, 42 out of 60 people want a new hero to be able to fly.
• In a survey of people who read Mysterious Planets, 14 out of 40 people want a new hero to be able to fly.

(3.) Do you think the proportion of all readers who want a new hero that can fly are nearly the same for the three different comic books? Explain your reasoning.

(4.) If you were in charge of these three comics, would you give the ability to fly to any of the new heroes? Explain your reasoning using the proportions you calculated.

The authors of The Adventures of Super Sam chose 50 different random samples of readers. Each sample was of size 20. They looked at the sample proportions who prefer the new hero to fly.

(6.) Are most of the sample proportions within 0.1 of your estimate for the population proportion?

(7.) If the authors of The Adventures of Super Sam give the new hero the ability to fly, will that please most of the readers? Explain your reasoning.

The authors of the other comic book series created similar dot plots.

(9.) Should the authors of either of these series give their new hero the ability to fly?

(10.) Why might it be more difficult for the authors of Mysterious Planets to make the decision than the authors of the other series?

Challenge #1

Tyler wonders what proportion of students at his school would dye their hair blue, if they were allowed to. He surveyed a random sample of 10 students at his school, and 2 of them said they would. Kiran didn’t think Tyler’s estimate was very accurate, so he surveyed a random sample of 100 students, and 17 of them said they would.

(1.) Based on Tyler’s sample, estimate what proportion of the students would dye their hair blue.

(2.) Based on Kiran’s sample, estimate what proportion of the students would dye their hair blue.

(3.) Whose estimate is more accurate? Explain how you know.

Challenge #2

The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5 and the IQR is 2. The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10 and the IQR is 1. If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate? Explain your reasoning.

Quiz Time