Section: 利用抽样数据估计人口比例 | 8.10 利用抽样数据估计人口比例-interactive

Section outline

Population Proportions
::人口比例

In this lesson, you will estimate population proportions. A population proportion is the ratio of members of the population with a certain attribute to the total number of members in the population. For example, this ratio could compare age, gender, or the people who support a candidate with the total number of members in the population.
::在此课程中,您将估算人口比例,人口比例是指与人口总数有一定关系的人口比例,例如,这个比例可以将年龄、性别或支持候选人的人与人口总数作比较。

You will be using sample proportions to estimate the population proportions. A sample proportion is the ratio of members in the sample with a certain attribute to the total number of members in the sample.
::您将使用抽样比例来估计人口比例。抽样比例是抽样成员的比例,与抽样成员总数有一定关系。

\begin{aligned} Population Proportion = \frac{Members in Population with Attribute}{Total Population} \\ Sample Proportion = \frac{Members in Sample with Attribute}{Total Sample} \end{aligned}

::人口比例人口比例 = 具有特征人口总数比例 = 具有属性人口总数比例 = 具有属性人口总数样本的抽样人口比例 =

S tatistics plays a vital role in monitoring endangered animals. When an animal is identified as endangered, scientists work to save the animal from extinction. This process begins with studying the factors which could cause the animal to become extinct . Scientists use sample proportions to estimate what part of the population is affected by these factors. You will explore this further later in the lesson.
::统计在监测濒危动物方面发挥着关键作用。当动物被确定为濒危动物时,科学家们努力保护动物免于灭绝。这一过程始于研究可能导致动物灭绝的因素。科学家们使用样本比例来估计哪些部分人口受到这些因素的影响。你将在课后进一步探讨这一点。

Tablets for Students
::学生平板

Example
::示例示例示例示例

The Norwood school district administrators are deciding on whether to buy tablet computers for all 8,000 students in the district. However, before purchasing the tablets, the administrators want to know what percentage of the parents and guardians have internet access at home so that students can do their homework on their tablets.
::诺伍德(Norwood)学校地区行政官员正在决定是否为该地区所有8 000名学生购买平板电脑。然而,在购买平板电脑之前,行政官员想知道家长和监护人中有多少人可以在家中上网,这样学生就可以在平板电脑上做功课。

A sample of 75 parents and guardians was taken from each of the three middle schools as well as the one high school. The number of parents and guardians with internet access is listed below. All decimals were rounded to the nearest hundredth.
::从三所中学和一所中学的每个中学抽取75个家长和监护人的样本,以下列出可上网的父母和监护人的人数,所有小数点四舍五入到最近的第100位。

$\begin{aligned} 74 / 75 \to 98.67 % \end{aligned}$
$\begin{aligned} 70 / 75 \to 93.33 % \end{aligned}$
$\begin{aligned} 72 / 75 \to 96 % \end{aligned}$
$\begin{aligned} 74 / 75 \to 98.67 % \end{aligned}$

Average $\begin{aligned} 72.5 / 75 \to 96.67 % \end{aligned}$
::平均平均数 72.5/75/7596.67%

From this survey , you can calculate that on average 72.5 parents and guardians from a sample 75 have internet access at home .
::从这次调查中,你可以计算出75个样本中平均有72.5个父母和监护人在家上网。

In order to estimate the total number of parents/guardians that have internet access in the entire population, use the proportion below:
::为了估计在总人口中能够上网的父母/监护人总数,请使用以下比例:

\begin{aligned} \frac{72.5}{75} & = \frac{x}{8, 000} \\ 72.5 \cdot 8, 000 & = 75 \cdot x \\ 580, 000 & = 75 x \\ 7, 733. \bar{3} & = x \end{aligned}

::72.575=8,00072.58,000=75x580,000=75x7,733.3 x

From the sample, school administrators can estimate that approximately 7,733 of the 8,000 students’ parents and guardians will have access to the internet. The school can expect that 67 parents and guardians will not have internet access.
::从抽样中,学校行政人员可以估计,8,000名学生的父母和监护人中约有7,733人可以上网。学校可以预计,67名家长和监护人不能上网。

Discussion Questions
::讨论问题讨论问题

This number isn’t exact. How could you get a better estimate?
::这个数字并不准确。您如何得到更好的估计 ?

Is it possible to get the exact number? Why or why not?
::能否得到确切数字?

Given these numbers, would you have the school district buy new tablets for all of the students? Explain your reasoning why.
::鉴于这些数字,你会让学校区为所有学生购买新的平板电脑吗?解释你的理由。

Polling
::投票投票

P olls are used to predict election outcomes. In this activity , you will use a sample proportion to predict the outcome of the Arizona senatorial race between Liam Coleman and Aarav Saxena.
::民意测验用来预测选举结果。在这一活动中,你将使用抽样比例来预测亚利桑那州利亚姆·科尔曼和阿拉夫·萨克森纳之间的参议员竞选结果。

Below are the mean results from taking 5 samples of 50 voters:
::以下是在50名选民中抽取5个样本的平均结果:

	Sample Votes	Population Projection
Liam Coleman	22
Aarav Saxena	28
Total	50	7,000,000

Using proportions, predict the number of votes that each candidate will receive in the election:
::使用比例,预测每个候选人在选举中将获得的选票数:

Liam Coleman
::利亚姆·科尔曼

\begin{aligned} \frac{Members in Sample with Attribute}{Total Sample} & = \frac{Members in Population with Attribute}{Total Population} \\ \frac{22}{50} & = \frac{x}{7, 000, 000} \\ 50 \cdot x & = 22 \cdot 7, 000, 000 \\ 50 x & = 154, 000, 000 \\ x & = 3, 080, 000 \end{aligned}

::具有 " 属性总数抽样 " 的抽样成员=具有 " 属性总数人口 " 的人口成员2250=7 000 00050x227 7 000 00050x=154 000 000x3 080 000

Aarav Saxena
::阿拉夫·萨塞纳

\begin{aligned} \frac{Members in Sample with Attribute}{Total Sample} & = \frac{Members in Population with Attribute}{Total Population} \\ \frac{28}{50} & = \frac{x}{7, 000, 000} \\ 50 \cdot x & = 28 \cdot 7, 000, 000 \\ 50 x & = 196, 000, 000 \\ x & = 3, 920, 000 \end{aligned}

::具有 " 属性总数抽样 " 的成员=具有 " 属性总数人口 " 的人口成员2850=7 000 00050x=287 7 7 000 00050x=196 000 000x=3 920 000

In these proportions , the members in the sample with the attribute are the number of votes the candidate received in the sample. The members in population with attribute is the projected number of votes that the candidate will receive from the entire population.
::在这些比例中,有属性的抽样成员为在抽样中候选人获得的选票数,有属性的成员为该候选人从全体人口获得的预计选票数。

	Sample Votes	Population Projection
Liam Coleman	22	3,080,000
Aarav Saxena	28	3,920,000
Total	50	7,000,000

Saved From Extinction
::从灭绝中保存

Among the largest threats to whales are pollution and poaching. Paul is a marine biologist studying the effects of pollution on whales. Paul knows that pollution can cause respiratory disease and lung cancer in whales. He wants to determine the number of whales that are affected by pollution.
::对鲸鱼的最大威胁是污染和偷猎。保罗是一位研究污染对鲸鱼的影响的海洋生物学家。保罗知道污染会导致鲸鱼呼吸道疾病和肺癌。他想确定受污染影响的鲸鱼数量。

Use the interactive below to take sample data that will help determine the number of whales affected by pollution.
::利用以下交互数据采集样本数据,帮助确定受污染影响的鲸鱼数量。

INTERACTIVE

Saved from Extinction

Drag the five red points to circle an area of the ocean to sample the number of whales.
::拖曳五个红点,以圆绕海洋的一个区域,对鲸鱼数量进行取样。

Click the white button to finish taking samples.
::单击白色按钮完成样本采集。

In the white boxes, enter the mean and MAD of the number of whales affected and unaffected by pollution between your samples.
::在白箱中,请输入受样品之间污染影响和未受污染影响的鲸鱼数量的平均值和MAD。

Enter the estimate of the number of whales affected by pollution in the ocean into the box when it appears.
::将受海洋污染影响的鲸鱼数量的估计数输入箱内。

Discussion Question
::讨论问题

Taking samples from one place may provide a smaller MAD value but it may not give you a good picture where the pollution is having an effect. How can you account for this?
::从一个地方采样可能提供较小的MAD值,但可能无法很好地描述污染的效应。您如何解释这一点 ?

Summary

A population proportion is the ratio of members of the population with a certain attribute to the total number of members in the population.
$\begin{aligned} Population Proportion = \frac{Members in the population with attribute}{Total population} \end{aligned}$

::人口比例是指人口成员比率,与人口成员总数有一定的关联。

A sample proportion is the ratio of members in the sample with a certain attribute to the total number of members in the sample.
$\begin{aligned} Sample Proportion = \frac{Members in the sample with attribute}{Total sample} \end{aligned}$

::抽样比例是抽样成员的比例,与抽样成员总数有一定的关联。抽样比例=具有属性的抽样成员。

Section outline

Population Proportions ::人口比例

Tablets for Students ::学生平板

Polling ::投票投票

Saved From Extinction ::从灭绝中保存

Population Proportions
::人口比例

Tablets for Students
::学生平板

Polling
::投票投票

Saved From Extinction
::从灭绝中保存