虚伪的假说

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Suppose you wanted to show that a coin was fair, what would be involved with setting up the experiment(s) to validate or deny the claim?
::假设你想证明硬币是公平的,建立验证或否认索赔的试验涉及什么?

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The Null Hypothesis 
::虚伪的假说

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One of the main uses for statistics is the testing of hypothesis. Commonly, a statement is made, such as “I think that the probability of a student in my class preferring red candy is less than 70%,” and experiments are conducted to determine the validity of the claim. However, to strengthen the results, specific steps should be followed as the experiment is set up, carried out, and reviewed or reported. The first step is the establishment of the null hypothesis notated as  $\begin{align*}H_0\end{align*}$ and alternative hypothesis , notated as $\begin{align*}H_1\end{align*}$ .
::统计的主要用途之一是对假设进行测试。 通常,人们会做出声明,比如“我认为班级学生更喜欢红糖的概率不到70% ” , 并进行实验以确定索赔的有效性。 但是,为了强化结果,在试验的建立、实施、审查或报告时,应该遵循具体步骤。 第一步是确定无效假设,称为H0, 替代假设,称为H1。

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• The null hypothesis , $\begin{align*}H_0\end{align*}$ , is known as "no-change"" or ""no-difference" hypothesis. Which means there is no statistical difference between two data sets. In the case of the claim above, the null hypothesis would be “The probability of a student in class preferring red candy is less than 70%”.
  ::无效假设H0被称为“不变”或“无差异”假设,这意味着两个数据集之间没有统计差异,就上述索赔而言,无效假设是“班级学生偏爱红糖的概率低于70%”。
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• The alternative hypothesis , $\begin{align*}H_1\end{align*}$ , is the clear and concise statement of the initial claim. In the case of the candy above, the hypothesis could be: “An average of 70% or greater of the students in school preferred candy to green candy,” or simply $\begin{align*}H_1 : p \ge 70\%\end{align*}$ , where  $\begin{align*}p\end{align*}$ stands for “ population percent”.
  ::另一种假说 — — H1 — — 是对最初索赔的简明扼要陈述。 在以上糖果的例子中,假设可以是 : “ 学校学生中平均有70%或70%以上喜欢糖果而不是绿色糖果 , ” 或者简单地说是H1:p70%,p代表“人口百分率 ” 。
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• It is extremely important that the alternative hypothesis and null hypothesis be mutually exclusive, meaning that if one is true, the other must be false.
  ::极其重要的是,替代假设和无效假设必须相互排斥,也就是说,如果一种假设是真实的,另一种假设必须是虚假的。

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In this lesson, you will practice identifying the null hypothesis for a number of claims.
::在这一教训中,你将实践确定若干索赔要求的无效假设。

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Assuming Null Hypotheses 
::假设假假假设

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The claim is made that a certain medication relieves headaches for more than 75% of patients who take it. What null hypothesis could be assumed during the investigation of this claim?
::声称某一种药物可以缓解75%以上服用药物的病人头痛。 在调查这一索赔时,可以假定什么是无效的假设?

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The null hypothesis for the claim “More than 75% of patients who take medication Z experience headache relief,” would be the mutually exclusive statement “75% or fewer of the patients who take medication Z experience headache relief”. This could be written as $\begin{align*}H_0:p \le 75\%\end{align*}$ .
::“接受Z类药物治疗的病人有75%以上头痛得到缓解”,这是“接受Z类药物治疗的病人有75%或更少头痛得到缓解”这一相互排斥的说法。 这种说法的无效假设可以写为H0:p75%。

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Creating Alternative and Null Hypotheses 
::创造替代和假假设

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A researcher wants to demonstrate that an average of more than 8 out of 10 dogs prefer the taste of a new dog food. What alternative hypothesis and null hypothesis might he work with? Use notation.
::研究者想证明,每10只狗中平均有8只多只狗更喜欢吃新狗的食物。他可以使用什么替代假设和无效假设?使用标记。

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The researcher’s hypothesis could be stated as: “On average, greater than 80% of dogs prefer the taste of dog food X.” In notation that would be:
::研究人员的假设可以说是: " 平均而言,超过80%的狗更喜欢吃狗食X。 "

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$$\begin{align*}H_1:p>80\%\end{align*}$$
::H1:p>80%

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The null hypothesis would be: “On average, 80% or fewer of dogs prefer the taste of dog food X.” In notation: $\begin{align*}H_0:p \le 80\%\end{align*}$ .
::无效的假设是:“平均而言,80%或更少的狗喜欢狗食X的味道。”

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Finding an  Alternative Hypothesis That Correlates to a Null Hypothesis
::寻找替代假设 与Null假设的相对应

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What alternative hypothesis would correlate to the null hypothesis $\begin{align*}H_0:p<60\%\end{align*}$ ?
::与无效假设H0:p<60%相关的替代假设是什么?

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If the null hypothesis is $\begin{align*}H_0: \mu < 60\%\end{align*}$ , then the alternative hypothesis is $\begin{align*}H_1:p \ge 60\%\end{align*}$ .
::如果无效假设是H0:%60%,那么替代假设是H1:p60%。

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Earlier  Problem Revisited
::重审先前的问题

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Suppose you wanted to show that a coin was fair, what would be the first steps involved with setting up the experiment(s) to validate or deny the claim?
::假设你想证明硬币是公平的,建立验证或否定索赔要求的试验的最初步骤是什么?

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The first step would be to identify the hypothesis and null hypothesis:
::第一步是确定假设和无效假设:

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$$\begin{align*}H_1:p &= 50\%\\ H_0:p & \neq 50\%\end{align*}$$
::H1:p=50%H0:p=50%

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Examples
::实例

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Example 1
::例1

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What is the null hypothesis to the claim that more people like cereal X than cereal Y?
::关于更多的人喜欢谷类X而不是谷类Y的说法,什么是无效的假设?

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The null hypothesis is the opposite of what you are hoping to claim, so  $\begin{align*}H_0\end{align*}$ : An equal number or m ore people like cereal Y than cereal X. 
::无效的假设与你想声称的相反, 所以H0:像谷类Y比谷类X一样多或同样多的人喜欢谷类Y。

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Example 2
::例2

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What alternative hypothesis would correlate to the null hypothesis $\begin{align*}H_0:0 \le \sigma \le 5\end{align*}$ ?
::与无效假设H0:0+5相关的替代假设是什么?

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$\begin{align*}H_1:0 > \sigma\end{align*}$  or  $\begin{align*}\sigma >5\end{align*}$
::H1:0或%5

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Example 3
::例3

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What alternative hypothesis and null hypothesis could be stated to define the claim that more people own blue cars than red cars? Use notation.
::可以用什么替代假设和无效假设来界定所谓拥有蓝色汽车的人多于红色汽车的人的说法?使用注释。

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$\begin{align*}H_0:R \ge B\end{align*}$  and $\begin{align*}H_1:R < B\end{align*}$
::H0:RB和H1:R<B

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Review 
::回顾

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For questions 1-8, state the null hypothesis for the given alternative hypothesis.
::对于问题1至8,指出对特定替代假设的无效假设。

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1. The number of sales of mp3 players would not go down if the price were raised by $10.
::1. 如果价格提高10美元,MP3球员的销售额不会下降。

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2. The average dog owner owns 2 or more cats.
::2. 平均狗主拥有2只或2只以上猫。

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3. The average cat owner does not own a dog.
::3. 平均猫主不拥有一只狗。

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4. The average subcompact car gets more than 30 mpg.
::4. 平均分包汽车得到超过30 mpg。

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5. The average computer gamer owns 4 or more games.
::5. 平均计算机游戏员拥有4场或4场以上游戏。

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6. The average temperature in Northern CO during the month of March is less than 70 degrees.
::6. 3月份北部CO的平均温度不到70度。

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7. At least 28% of astronomers can name more than 50 stars.
::7. 至少28%的天文学家可以命名50多个恒星。

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8. Less than 35% of astronomers can name at least 75 stars.
::8. 不到35%的天文学家可以点出至少75颗恒星的名称。

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For questions 9-16, use notation to state the alternative hypothesis and null hypothesis.
::对于问题9-16,使用注解来说明替代假设和无效假设。

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9. Less than 1% of U.S. citizens participate in a militia.
::9. 不到1%的美国公民参加民兵。

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10. Between 20% and 35% of students watch cartoons on Saturday morning.
::10. 20%至35%的学生在星期六早上观看漫画。

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11. More than 71% of high school students can name a favorite fantasy book.
::11. 超过71%的高中学生可以命名一本最喜欢的幻想书。

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12. Less than 1 in 5 U.S. college students ride a bike to school.
::12. 5名美国大学生中只有不到1人骑自行车上学。

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13. Less than 2% of U.S. adults have milked a cow.
::13. 不到2%的美国成年人挤奶了一头奶牛。

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14. Between 2% and 10% of Americans are vegetarians.
::14.2%至10%的美国人是素食主义者。

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15. Less than 4% of high school students take Statistics.
::15. 不到4%的高中学生接受统计。

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16. More than 80% of students say they learn better through video than with a textbook.
::16. 80%以上的学生说,他们通过视频比用教科书学习更好。

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Review (Answers)
::回顾(答复)

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Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。