Difference between revisions of "Manuals/calci/CONFIDENCE"

Revision as of 00:33, 31 March 2014

CONFIDENCE(a,sd,s)

This function gives value of the confidence intervals.
Confidence intervals are calculated based on the standard error of a measurement.
It is measures the probability that a population parameter will fall between lower bound and upper bound of the values.
There are four steps to constructing a confidence interval.

   1. Identify a sample statistic.
   2. Select a confidence level. 
   3. Find the margin of error.
   4. Specify the confidence interval.

Normally once standard error value is calculated, the confidence interval is determined by multiplying the standard error by a constant that reflects the level of significance desired, based on the normal distribution.
In $CONFIDENCE(a,sd,s)$ , $a$ is the alpha value which is indicating the significance level used to find the value of the confidence level.
It equals $100*(1-alpha)\%$ , or alpha of 0.05 indicates a 95 percent confidence level.
This value is $\pm$ 1.96
$sd$ is the standard deviation of the population for the data range.
$s$ is the size of the sample.
Confidence interval is calculated using the following formula:

     $Confidenceinterval=samplestatistic+Marginoferror$ .

 1. Any one of the argument is nonnumeric. 
 2.Suppose  $0\leq alpha\leq 1$ 
 3. value of s is less than 1.

Suppose with the population of 10 for the standard deviation 3.2, with the alpha value 0.2 then, CONFIDENCE(0.2,3.2,10) =1.296839.
So the Confidence interval value is $10\pm 1.296839=approximately[11.29,8.70]$ .

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 *In <math>CONFIDENCE(a,sd,s)</math> , <math>a</math> is the alpha value which is indicating the significance level used to find the value of the confidence level.
 *It equals <math>100*(1-alpha)%</math>, or alpha of 0.05 indicates a 95 percent confidence level.
-*This value is <math> \plusmn</math> {1.96}
+*This value is <math> \pm </math> 1.96
 *<math> sd </math> is the standard deviation of the population for the data range.
 *<math> s </math> is the size of the sample.
 *Confidence interval is calculated using the following formula:
       <math>Confidence interval = sample statistic + Margin of error</math>.
-*So  <math> confidence interval =\bar{x}\plusmn {1.96}(\frac{\sigma}{\sqrt {s}})</math>
+*So  <math> confidence interval =\bar{x}\pm 1.96(\frac{\sigma}{\sqrt {s}})</math>
 *where <math>\bar{x}</math> is the sample mean,sigma is the standard deviation.
 *This function will give the result as error when