这部分需要会什么？
- 区分总体、样本和样本统计量
- 理解随机抽样与随机分组各自支持的结论
- 解释误差范围并识别样本偏差
核心概念与公式
总体是希望研究的全体对象，样本是实际观测的一部分。随机抽样有助于把结果推广到所抽取的总体；随机分配处理的设计良好的对照实验，有助于判断处理造成的因果影响。这两种随机化用途不同。
估计值加减误差范围构成报告区间，例如 52% ± 3 个百分点给出 49% 至 55%。相同抽样方式和置信水平下，样本量增大通常减小抽样误差；常见情况下误差范围约与样本量平方根成反比。
做题时怎样使用
- 先确定研究希望推广到谁，以及样本实际上来自谁
- 检查随机抽样、非应答和自愿参与等因素
- 只作研究设计支持的结论，读清误差范围的单位与置信条件
容易混淆的地方
样本很大不能自动消除抽样偏差。观察到相关关系不能直接断言因果；误差区间也不是对总体参数位置的绝对保证。
用一个例题串起方法
知识点教学例题从某校全体学生中随机抽取 400 人，估计支持某方案的比例为 58%，误差范围为 4 个百分点。报告区间是什么，能直接推广到全国学生吗？
展开解题思路 ＋
报告区间为 \(58\%-4\%=54\%\) 至 \(58\%+4\%=62\%\)。样本来自这一所学校，推断范围应对应这所学校的学生，不能直接推广到全国学生。
本知识点题库
先独立作答，再查看答案与解析。
抽样・推断与误差范围进阶
A town manager selected 2 random samples of residents in the town to estimate the percentage of all residents that planned to vote in favor of a new business in the downtown area. Based on the first sample, he estimated that 75% of the residents in the town planned to vote in favor; with an associated margin of error of 8.5%.Based on the second sample, he estimated that 83% of the residents in the town planned to vote in favor, with an associated margin of error of 6.9%. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a larger margin of error than the second sample?
原库参考解析
抽样・推断与误差范围进阶
A company studied a random sample of 72 lawns in a small town. The company found that 9 of these lawns contain acidic soil. If there are 1,080 lawns in the town, which of the following is the best estimate of the number of lawns that contain acidic soil?
原库参考解析
抽样・推断与误差范围进阶
A district school board in a certain state is proposing a change to the length of lunch periods for all high schools in the district. A sample of 365 high school students was selected at random from all high school students in the district. The selected students were asked whether they approved of the proposed change, and 211 students responded that they did not approve. Which of the following is the largest population to which the results of the survey can be generalized?
原库参考解析
抽样・推断与误差范围进阶
A company that produces only one type of item wants to estimate the percent of the items produced in a typical week that are defective. A random sample of 540 of the items produced in a certain week were tested. Based on the sample, it is estimated that 12.5% of all items produced by the company in this week are defective, with an associated margin of error of 2.79%. Based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all items produced by the company during this week?
原库参考解析
抽样・推断与误差范围进阶
A sample was selected at random from a population. Based on the sample, it is estimated that the mean value of a variable for this population is 88, with an associated margin of error of 1.5. Based on the estimate and associated margin of error, which of the following best describes the range of plausible values for the population mean?
原库参考解析
抽样・推断与误差范围挑战
For a study, a group of chipmunks will be selected from a habitat consisting of 220 chipmunks, and a group of prairie dogs will be selected from a habitat consisting of 190 prairie dogs. Some of the chipmunks and prairie dogs will be in a treatment group, and some of the chipmunks and prairie dogs will be in a control group. Which of the following is necessary for this study to attempt to establish a cause-and-effect relationship between two variables?
原库参考解析
抽样・推断与误差范围进阶
A survey was conducted in Arlington to estimate the percent of adult residents who support the addition of a community pool in their town. Based on the survey, it is estimated that 40% of all adult residents of Arlington support the addition of a community pool in their town, with an associated margin of error of 7%. Which of the following is the most appropriate conclusion about all adult residents of Arlington?
原库参考解析
抽样・推断与误差范围挑战
The manager of a gym selected a sample of 142 members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that 89% of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of 5.15%. If the survey is repeated with a random sample of 284 members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?
原库参考解析
抽样・推断与误差范围挑战
For a survey, a sample of 1,018 people was selected at random from all registered voters in a county. Based on the survey, it is estimated that 66% of all registered voters in the county are in favor of a new law, with an associated margin of error of 2.91%. Which of the following best describes the plausible values for the percent of all registered voters in the county who are in favor of the new law?
原库参考解析
抽样・推断与误差范围挑战
A research manager selected 2 random samples of ovens of a certain type to estimate the average amount of time this type of oven takes to preheat to 325 degrees Fahrenheit (°F). The research manager recorded the amount of time, in minutes, each oven takes to preheat to 325 °F. Based on the first sample, the research manager estimated that this type of oven takes an average of 15.2 minutes to preheat to 325 °F, with an associated margin of error of 1 minute. Based on the second sample, the research manager estimated that this type of oven takes an average of 15.4 minutes to preheat to 325 °F, with an associated margin of error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a smaller margin of error than the second sample?
原库参考解析
抽样・推断与误差范围进阶
A machine fills bags with approximately 11 ounces of walnuts. To test the accuracy of the filling process, 330 bags of walnuts were selected at random and weighed. Based on the sample, it is estimated that the average weight of all bags of walnuts filled by the machine in an 8-hour period is 11.17 ounces, with an associated margin of error of 0.2 ounce. Which of the following is the best interpretation of this estimate?
原库参考解析
抽样・推断与误差范围挑战
The manager of a gym selected a sample of 159 members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that 88% of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of 5.05%. If the survey is repeated with a random sample of 318 members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?
原库参考解析
