AP Statistics Curriculum 2007 Estim Proportion - Revision history

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

2020-03-03T16:45:39Z

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

2011-03-11T01:32:35Z

‎Sample-Size Estimation

2011-03-11T01:29:10Z

‎Sample-Size Estimation

2011-03-11T01:28:25Z

‎Sample-size Estimation

2011-03-11T01:28:08Z

‎Sample-size Estimation

2011-03-11T01:27:30Z

‎Sample-size Estimation

2011-03-11T01:25:27Z

‎Sample-size Estimation

2011-03-11T01:23:41Z

‎Sample-size Estimation

2011-03-11T01:17:12Z

‎Sample-size Estimation

2011-03-11T01:16:31Z

‎Sample-Size Estimation

← Older revision		Revision as of 16:45, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ====Sample-Size Estimation====
 How many subjects are needed if the heart-researchers want <math>ME < 0.005</math> for a 95% CI, and have a guess based on previous research that <math>\tilde{p}= 0.04</math>?
-: <math>n \geq {0.04(1-0.04)\over {1.96^2\times 0.005^2}} - 1.96^2=395.9918 \approx 396.</math>
+: <math>n \geq {1.96^20.04(1-0.04)\over {0.005^2}} - 1.96^2= 5896.856 \approx 5897.</math>
 ====Siblings Genders====

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 ===Examples===
 ====Sample-Size Estimation====
-How many subjects are needed if the heart-researchers want <math>SE < 0.005</math> for a 95% CI, and have a guess based on previous research that <math>\tilde{p}= 0.04</math>?
+How many subjects are needed if the heart-researchers want <math>ME < 0.005</math> for a 95% CI, and have a guess based on previous research that <math>\tilde{p}= 0.04</math>?
 : <math>n \geq {0.04(1-0.04)\over {1.96^2\times 0.005^2}} - 1.96^2=395.9918 \approx 396.</math>

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 This equation has one unknown parameter (n), which we can solve for if we are given an upper limit for the margin of error (remember that the critical value <math>z_{\alpha\over 2} \approx 2</math>):
-: <math>ME \geq  z_{\alpha \over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2} \longrightarrow n \geq z_{\alpha \over 2}^2{\tilde{p}(1-\tilde{p})\over {SE_{\tilde{p}}^2} } -z_{\alpha \over 2}^2.</math>
+: <math>ME \geq  z_{\alpha \over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2} \longrightarrow n \geq z_{\alpha \over 2}^2{\tilde{p}(1-\tilde{p})\over {ME^2} } -z_{\alpha \over 2}^2.</math>
 ===Examples===

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 For a given margin of error (ME) we can derive the minimum sample-size that guarantees an interval estimate within the given margin of error. The margin of error (ME) is the product of the critical value (t or z) and the standard-error of the sample-proportion:
-: <math>z_{\alpha\over 2}\times SE_{\tilde{p}} =  z_{\alpha\over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2}.</math>
+: <math>ME = z_{\alpha\over 2}\times SE_{\tilde{p}} =  z_{\alpha\over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2}.</math>
 This equation has one unknown parameter (n), which we can solve for if we are given an upper limit for the margin of error (remember that the critical value <math>z_{\alpha\over 2} \approx 2</math>):

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 : <math>z_{\alpha\over 2}\times SE_{\tilde{p}} =  z_{\alpha\over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2}.</math>
-This equation has one unknown parameter (n), which we can solve for if we are given an upper limit for the margin of error. The critical value <math>z_{\alpha\over 2} \approx 2</math>, and
+This equation has one unknown parameter (n), which we can solve for if we are given an upper limit for the margin of error (remember that the critical value <math>z_{\alpha\over 2} \approx 2</math>):
-: <math>z_{\alpha\over 2}\times SE_{\tilde{p}} \geq  2\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2} \longrightarrow n \geq {\tilde{p}(1-\tilde{p})\over {4SE_{\tilde{p}}^2} } -z_{\alpha \over 2}^2.</math>
+: <math>z_{\alpha\over 2}\times SE_{\tilde{p}} \geq  z_{\alpha \over 2}\sqrt{\tilde{p}(1-\tilde{p})\over n+z_{\alpha \over 2}^2} \longrightarrow n \geq {\tilde{p}(1-\tilde{p})\over {z_{\alpha \over 2}SE_{\tilde{p}}^2} } -z_{\alpha \over 2}^2.</math>
 ===Examples===