10.3 反面

章节大纲

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  How many tails are there in the test for the claim: “Less than 5% of high school students are familiar with the tails of a distribution ?”
  ::在索赔的测试中有多少尾巴:“不到5%的中学生熟悉分布的尾巴?”

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  Tails 
  ::反反面

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  The “tails” of a test are the values outside of the critical values . In other words, the tails are the ends of the distribution, and they begin at the greatest or least value included in the alternative hypothesis (the critical values).
  ::测试的“尾部”是关键值之外的值。 换句话说,尾部是分布的终点,它们以替代假设(关键值)中包含的最大或最小值开始。

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  In the graph below, the tails are in red and the rest of the distribution is in green. The critical values of the test in the image are -8 and 28, as these are the dividers between values supporting the alternative and null hypothesis . The area in red can also be seen as the rejection region , since an observed value in this region indicates that the null hypothesis be rejected.
  ::在下图中,尾巴为红色,其余的分布为绿色。图像中测试的关键值是 - 8 和 28, 因为这些是支持替代假设和无效假设的值之间的分隔符。 红色区域也可以被视为拒绝区域, 因为观察到的该区域值表明拒绝无效假设。

  

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  There are three types of test from a “tails” standpoint:
  ::从“尾数”的角度来看,检验有三种类型:

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  • A left-tailed test only has a tail on the left side of the graph:
    ::左尾试验在图左侧只有尾巴:

  

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  • A right-tailed test only has a tail on the right side of the graph:
    ::右尾部测试在图的右侧只有尾巴:

  

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  • A two-tailed test has tails on both ends of the graph. This is a test where the null hypothesis is a claim of a specific value. For example: $\begin{array}{r}{H}_0:X=5\end{array}$
    ::两尾试验在图形的两端都有尾巴。这是无效假设是特定价值要求的试验。例如: H0:X=5

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  Determining the Null Hypothesis and Kind of Test 
  ::确定努尔假设和试验类型

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  1. A researcher claims that black horses are, on average , more than 30 lbs heavier than white horses, which average 1100 lbs. What is the null hypothesis, and what kind of test is this?
  ::1. 一名研究人员声称,黑马平均比白马重30磅以上,平均重1 100磅。

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  The null hypothesis would be notated $\begin{array}{r}{H}_0:\mu \le 1130lbs\end{array}$
  ::无效的假设将被评分 H0:\\\\\\1130 lbs

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  This is a right-tailed test, since the tail of the graph would be on the right. Recognize that values above 1130 would indicate that the null hypothesis be rejected, and the red area represents the rejection region .
  ::这是一个直接的测试, 因为图的尾部在右侧。 认识到1130以上值将表明无效假设被否决, 红色区域代表拒绝区域 。

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  2. A package of gum claims that the flavor lasts more than 39 minutes. What would be the null hypothesis of a test to determine the validity of the claim? What sort of test is this?
  ::2. 一套口香糖声称口香糖的口香糖口味持续超过39分钟。检验确定索赔的有效性的无效假设是什么?这是什么样的检验?

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  The null hypothesis would by notated as $\begin{array}{r}{H}_0:\mu \le 39\end{array}$ .
  ::无效假设是H0: @______BAR___BAR__BAR__H0:___BAR___BAR___BAR_H0:_BAR___BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_

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  This is a right-tailed test, since the rejection region would consist of values greater than 39.
  ::这是一个直接的检验标准,因为拒绝区域将包含超过39个的数值。

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  3. An ice pack claims to stay cold between 35 and 65 minutes. What would be the null hypothesis of a test to determine the validity of the claim? What sort of test would it be?
  ::3. 冰块声称在35至65分钟之间保持寒冷。 检验确定索赔有效性的无效假设是什么?它将是什么类型的检验?

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  The null hypothesis would be $\begin{array}{r}{H}_0:35>\mu \cup \mu >65\end{array}$ .
  ::无效假设是H0: 3565

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  This is a two-tailed test, since the null hypothesis contains the values above and below a given range .
  ::这是一个双重的检验标准,因为无效假设包含某一范围以上和以下的数值。

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  Earlier Problem Revisited
  ::重审先前的问题

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  How many tails are there in the test for the claim: “Less than 5% of high school students are familiar with hypothesis tails?”
  ::在索赔的测试中有多少尾巴:“只有5%以上的中学生熟悉假想尾巴?”

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  This is a left-tailed test, since the null hypothesis is $\begin{array}{r}{H}_0:X\ge 5\mathrm{\%}\end{array}$  meaning that the rejection region contains only values below a given value.
  ::这是一个左尾试验, 因为无效假设是 H0:X5% 意味着拒绝区域仅包含低于给定值的值 。

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  Examples 
  ::实例

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  For each question: a) State the null and alternative hypothesis for a test to determine the validity of the claim, and b) Identify left, right, or two-tailed test type.
  ::对于每个问题a) 说明用于确定索赔有效性的试验的无效假设和替代假设;(b) 标明左、右或双尾试验类型。

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  Example 1
  ::例1

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  The weatherman claims an average of 2" - 2.5" of snow throughout the country.
  ::天气预报员声称全国平均有 2" -2.5"的雪。

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  a)  $\begin{array}{r}{H}_1:2^{\mathrm{\prime }\mathrm{\prime }}<\mu <{2.5}^{\mathrm{\prime }\mathrm{\prime }}\end{array}$ and $\begin{array}{r}{H}_0:2^{\mathrm{\prime }\mathrm{\prime }}>\mu \cup \mu >{2.5}^{\mathrm{\prime }\mathrm{\prime }}\end{array}$
  :a) H1:2____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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  b) This is a two-tailed test, since the rejection region is at the ends of the graph.
  :b) 这是一个双尾测试,因为拒绝区域位于图的末尾。

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  Example 2
  ::例2

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  The average Siberian Husky weighs more than 35 pounds.
  ::西伯利亚海斯基的平均体重超过35磅

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  a)  $\begin{array}{r}{H}_1:\mu >35lbs\end{array}$ and $\begin{array}{r}{H}_0:35lbs\ge \mu \end{array}$
  :a) H1:35磅和H0.35磅

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  b) This is a right-tailed test, since the rejection region is located on the right end of the graph.
  :b) 由于拒绝区域位于图的右端,因此这是一个直接的试验。

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  Example 3
  ::例3

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  The United Parcel Service claims less then 5-day shipping times for ground packages.
  ::United Parcel Service要求赔偿地面包件的5天运输时间少于5天。

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  a)  $\begin{array}{r}{H}_1:\mu <5days\end{array}$ and $\begin{array}{r}{H}_0:\mu \ge 5days\end{array}$
  :a) H1:5天和H:5天

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  b) This is a left-tailed test, since the ‘reject’ values are on the left end of the graph.
  :b) 这是一个左尾试验,因为 " 反向 " 值在图的左端。

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  Review 
  ::回顾

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  For each question: a) State the null and alternative hypothesis for a test to determine the validity of the claim, and b) Identify left, right, or two-tailed test type.
  ::对于每个问题a) 说明用于确定索赔有效性的试验的无效假设和替代假设;(b) 标明左、右或双尾试验类型。

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  1. The average miniature horse is less than 34 inches at the shoulder. Tiny Equines claims that their miniature horses are an average of 3 inches less than the breed average.
     ::平均迷你马肩部小于34英寸。 小母马声称他们的迷你马平均比繁殖平均小3英寸。
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  2. Speedy Solutions is a delivery company that claims all deliveries average less than 72 hours.
     ::快速解决方案公司是一个交货公司,要求所有交货平均少于72小时。
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  3. Terrific Textiles claims that 45% to 55% of t-shirts sold in CO are red.
     ::超级纺织公司声称,在以CO出售的T恤衫中,45%至55%是红色的。
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  4. Gas Hater Car Sales claims that 70% or more of the cars on the lot average more than 40 mpg.
     ::Gaser Hater汽车销售公司声称,批量中70%或以上的汽车平均超过40 mpg。
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  5. The 2011 average service time for Fast Fatz Burgers was 56 seconds. The store manager claims that the 2012 average is more than 5 seconds faster.
     ::Fast Fatz Burgers 2011 年的平均服务时间为 56 秒,商店经理声称2012 年的平均服务时间比 5 秒快。
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  6. Colorful Cavity Causers sells multi-colored candies by the bag. Each bag is claimed to average between 5.5 and 6.5 oz.
     ::包包出售多色糖果,每个包平均在5.5至6.5 oz之间。
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  7. Aaron works for an electronics company, quality-testing batteries. The company claims a minimum of 5 hrs battery life.
     ::Aaron在一家电子公司工作 质量测试电池 该公司要求至少5小时电池寿命
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  8. The lessons in this Probability and Statistics text average 13 practice problems each.
     ::这一概率和统计文本中的经验教训平均各有13个实践问题。
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  9. The outside temperature in Maui averages between 72 and 83 degrees year-round.
     ::毛伊岛的外部温度全年平均为72至83度。
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  10. 72% of elementary school teachers are female.
      ::72%的小学教师是女性。
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  11. Graph Below
      
      
      
      ::下图图图图如下
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  12. Graph Below
      
      
      
      ::下图图图图如下
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  13. Graph Below

      
      

      
      
      ::下图图图图如下

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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 。