AP Statistics Curriculum 2007 Hypothesis L Mean - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T21:19:56Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

IvoDinov: /* Hypothesis Testing About a Mean: Large Samples */

2013-05-22T15:54:54Z

‎Hypothesis Testing About a Mean: Large Samples

IvoDinov: /* Hypothesis Testing About a Mean: Large Samples */

2013-05-22T15:54:43Z

‎Hypothesis Testing About a Mean: Large Samples

IvoDinov: /* Example */

2012-03-02T16:44:24Z

‎Example

IvoDinov: /* Cavendish Mean Density of the Earth */

2011-02-28T16:51:11Z

‎Cavendish Mean Density of the Earth

IvoDinov: /* Examples */ added an example: US Federal Budget Deficit

2011-02-23T19:32:52Z

‎Examples: added an example: US Federal Budget Deficit

Jenny at 20:40, 28 June 2010

2010-06-28T20:40:52Z

Jenny at 17:24, 28 June 2010

2010-06-28T17:24:14Z

IvoDinov: /* Parallels between Hypothesis Testing and Confidence Intervals */

2009-10-26T05:12:16Z

‎Parallels between Hypothesis Testing and Confidence Intervals

IvoDinov: ad

2009-10-26T05:11:47Z

← Older revision		Revision as of 21:19, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=AP_Statistics_Curriculum_2007_Hypothesis_L_Mean}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Hypothesis_L_Mean}}

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 * Alternative Research Hypotheses:
 ** One sided (uni-directional): <math>H_1: \mu >\mu_o</math>, or <math>H_1: \mu<\mu_o</math>
-** Double sided: \)H_1: \mu \not= \mu_o\)
+** Double sided: \(H_1: \mu \not= \mu_o\)
 ====Known Variance====

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 * Alternative Research Hypotheses:
 ** One sided (uni-directional): <math>H_1: \mu >\mu_o</math>, or <math>H_1: \mu<\mu_o</math>
-** Double sided: <math>H_1: \mu \not= \mu_o</math>
+** Double sided: \)H_1: \mu \not= \mu_o\)
 ====Known Variance====

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 As the population variance is not given, we have to use the [[AP_Statistics_Curriculum_2007_StudentsT |T-Statistics]]: <math>T_o = {\overline{x} - \mu_o \over SE(\overline{x})} \sim T(df=29)</math>
 : <math>T_o = {\overline{x} - \mu_o \over SE(\overline{x})} = {14.77 - 20 \over {{1\over \sqrt{30}} \sqrt{\sum_{i=1}^{30}{(x_i-14.77)^2\over 29}}})}=-1.733</math>.
-: <math>P(T_{(df=29)}>T_o=-1.733)=0.047</math>, thus
+: <math>P(T_{(df=29)} < T_o=-1.733)=0.047</math>, thus
 : the <math>p-value=2\times 0.047= 0.094</math> for this (double-sided) test.

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 ====Cavendish Mean Density of the Earth====
-A number of famous early experiments of measuring physical constants has later been shown to be biased. In the 1700's [http://en.wikipedia.org/wiki/Henry_Cavendish Henry Cavendish] measured the [http://www.jstor.org/stable/pdfplus/107617.pdf Mean density of the Earth]. Formulate and test null and research hypotheses about these data regarding the now known exact mean-density value = 5.517. These sample statistics may be helpful
+A number of famous early experiments of measuring physical constants has later been shown to be biased. In the 1700's [http://en.wikipedia.org/wiki/Henry_Cavendish Henry Cavendish] measured the [http://www.jstor.org/stable/pdfplus/107617.pdf Mean density of the Earth]. Formulate and test null and research hypotheses about these data regarding the now known exact mean-density value = 5.517. These sample statistics may be helpful (you can also find the [[AP_Statistics_Curriculum_2007_Hypothesis_L_Mean_Tbl1_tr|transposed table here]]):
 : n = 23, sample mean = 5.483,    sample SD = 0.1904
 <center>

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 |}
 </center>
 <hr>

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 ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Testing a Claim About a Mean: Large Samples==
-We already saw [[AP_Statistics_Curriculum_2007_Estim_L_Mean | how to construct point and interval estimates for the population mean in the large sample case]]. Now, we show how to do hypothesis testing about the mean for large sample-sizes.
+We already saw [[AP_Statistics_Curriculum_2007_Estim_L_Mean | how to construct point and interval estimates for the population mean in the large sample case]]. Now, we show how to do hypothesis testing of the mean for large sample-sizes.
 ===[[AP_Statistics_Curriculum_2007_Estim_L_Mean |  Background]]===

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 ===Example===
-Let's [[AP_Statistics_Curriculum_2007_Estim_L_Mean#Example | revisit the ''number of sentences per advertisement'' example]], where we measure of readability for magazine advertisements.  A random sample of the number of sentences found in 30 magazine advertisements is listed below.  Suppose:
+Let's [[AP_Statistics_Curriculum_2007_Estim_L_Mean#Example | revisit the ''number of sentences per advertisement'' example]], where we measure the readability for magazine advertisements.  A random sample of the number of sentences found in 30 magazine advertisements is listed below.  Suppose:
 : We want to test at <math>\alpha=0.05</math>
 : Null hypothesis: <math>H_o: \mu=20</math>
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 : the <math>p-value=2\times 0.047= 0.094</math> for this (double-sided) test.
-Therefore, we '''can not reject''' the null hypothesis at <math>\alpha=0.05</math>! The left and right white areas at the tails of the T(df=29) distribution depict graphically the probability of interest, which represents the strength of the evidence (in the data) against the Null hypothesis. In this case, the cumulative tail area is 0.094, which is larger than the initially set [[AP_Statistics_Curriculum_2007_Hypothesis_Basics | Type I]] error <math>\alpha = 0.05</math> and we can not reject the null hypothesis.
+Therefore, we '''can not reject''' the null hypothesis at <math>\alpha=0.05</math>! The left and right white areas at the tails of the T(df=29) distribution depict graphically the probability of interest, which represents the strength of the evidence (in the data) against the Null hypothesis. In this case, the cumulative tail area is 0.094, which is larger than the initially set [[AP_Statistics_Curriculum_2007_Hypothesis_Basics | Type I]] error <math>\alpha = 0.05</math> so we can not reject the null hypothesis.
 <center>[[Image:SOCR_EBook_Dinov_Hypothesis_020508_Fig3.jpg|600px]]</center>
-* You can see use the [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses (One-Sample T-Test)] to carry out these calculations as shown in the figure below.
+* You can use the [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses (One-Sample T-Test)] to carry out these calculations as shown in the figure below.
 <center>[[Image:SOCR_EBook_Dinov_Hypothesis_020508_Fig2.jpg|600px]]</center>
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 ====Cavendish Mean Density of the Earth====
-A number of famous early experiments of measuring physical constants have later been shown to be biased. In the 1700's [http://en.wikipedia.org/wiki/Henry_Cavendish Henry Cavendish] measured the [http://www.jstor.org/stable/pdfplus/107617.pdf Mean density of the Earth]. Formulate and test null and research hypotheses about these data regarding the now know exact mean-density value = 5.517. These sample statistics may be helpful
+A number of famous early experiments of measuring physical constants has later been shown to be biased. In the 1700's [http://en.wikipedia.org/wiki/Henry_Cavendish Henry Cavendish] measured the [http://www.jstor.org/stable/pdfplus/107617.pdf Mean density of the Earth]. Formulate and test null and research hypotheses about these data regarding the now known exact mean-density value = 5.517. These sample statistics may be helpful
 : n = 23, sample mean = 5.483,    sample SD = 0.1904
 <center>

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 * Hypothesis (Significance) testing: Only one possible value for the parameter, called the hypothesized value, is tested. We determine the strength of the evidence (confidence) provided by the data against the proposition that the hypothesized value is the true value.
-===[[EBook_Problems_Hypothesis_L_Mean|Problems]==
+===[[EBook_Problems_Hypothesis_L_Mean|Problems]]===
 <hr>

← Older revision		Revision as of 05:11, 26 October 2009
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	* Hypothesis (Significance) testing: Only one possible value for the parameter, called the hypothesized value, is tested. We determine the strength of the evidence (confidence) provided by the data against the proposition that the hypothesized value is the true value.		* Hypothesis (Significance) testing: Only one possible value for the parameter, called the hypothesized value, is tested. We determine the strength of the evidence (confidence) provided by the data against the proposition that the hypothesized value is the true value.
		+
		+	===[[EBook_Problems_Hypothesis_L_Mean\|Problems]==

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