Manuals/calci/CONFIDENCE

CONFIDENCE(a,sd,s)

• $a$ is alpha value which is indicating the significance level.
• $sd$ is the standard deviation.
• $s$ is the size of the sample.

Description

• 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
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sd } is the standard deviation of the population for the data range.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s } is the size of the sample.
• Confidence interval is calculated using the following formula:

    Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Confidence interval = sample statistic + Margin of error}
. 

• So Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle confidence interval =\bar{x}\pm 1.96(\frac{\sigma}{\sqrt {s}})}
• where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{x}} is the sample mean,sigma is the standard deviation.
• This function will give the result as error when

 1. Any one of the argument is nonnumeric. 
 2.Suppose Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0\le alpha\le1 }

 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10\pm 1.296839= approximately[11.29,8.70]} .

Examples

1. =CONFIDENCE(0.6,4.6,20) = 0.539393789
2. =CONFIDENCE(0.09,8.1,25) = 2.746544290
3. =CONFIDENCE(0.001,18.8,50) = 8.74859415

See Also

• ZTEST
• ZTESTEQUALMEANS

References

CONFIDENCE