Tests concerning a Population Proportion

# Tests concerning a Population Proportion - Tests concerning...

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Unformatted text preview: Tests concerning a Population Proportion Background: Large Sample Tests Common large sample test statistics have form Z = ¡ ¢ £ ¤ ¡ . ¥ ¦ is the estimator for the population parameter of interest. ¥ § is the expected value under the Null Hypothesis. ¨ © ¡ is standard deviation of the estimator (or an estimate of it) Binomial proportion: parameter ª« The foundation for the test is the unbiased estimator « ¬ ­ ®¯° . «ª±²³´µ¶²·ª above so « ¬ª±²³´µ¶²·ª¸ ¡ « £ ª±²³´µ¶²·ª £ ¹« £ º» ¼ « £ ½ ° ¾ ±²³´µ¶²·ª¤ ¡ Null Hypothesis: ¿ £ À « ­ « £ Test statistic value: z = « ¬¢« £ ª ¹« £ º»¢« £ ½ ° ¾ Valid provide °« £ Á »ÂªÃ°Äª°º» ¼ « £ ½ Á »Â Alternative Hypothesis Rejection Region Å Æ À Ç È ª Ç É Ê È ªÊ Æ Å Æ À Ç Ë ª Ç É Ê Ë ªÊ Æ Å Æ À Ç Ì ª Ç É ÍÎÏÐÍÑªÊ Ë ªÊ Æ Ò ¾ ªÓÑ Ê È ªÊ Æ Ò ¾ Large Sample Obesity example The Associate Press (Oct 9, 2002) reported in a sample of 4115 American adults, 1276 were found to be obese (body mass index > 30 kg/m 2 ). # Body mass index calculation # BMI = ( weight(lbs) / height(inches)**2 ) * 703(conversion factor) 28.1 = ( 190 / 69**2 ) * 703 Test the null hypothesis that proportion of the American adults that is obese is .3 versus the alternative that proportion greater than .3 using a significance level of .10. Steps 1. p = proportion of American adults that are obese. 2. ¡ ¢ £ ¤ ¥¦ 3. § ¨ ¢ £ © § ¥¦ 4. Since ª« ¬ ¤ §§­®®¯ °¥ ± ² ®³§ and ª´® µ « ¬ ¶ ¤ ­®®¯ °¥ ·§ ² ®³ the large sample test statistic can be used....
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## This note was uploaded on 12/20/2011 for the course STAT 344 taught by Professor Staff during the Spring '08 term at George Mason.

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Tests concerning a Population Proportion - Tests concerning...

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