Manuals/calci/CONFIDENCE

CONFIDENCE (Alpha,StandardDeviation,Size)

• $Alpha$ is alpha value which is indicating the significance level.
• 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 StandardDeviation} is the value of the standard deviation.
• 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 Size} 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 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 (Alpha,StandardDeviation,Size)} , 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 Alpha} is the alpha value which is indicating the significance level used to find the value of the confidence level.
• It equals 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 100*(1-Alpha)%} , or alpha of 0.05 indicates a 95 percent confidence level.
• This 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 \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 StandardDeviation } 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 Size } 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 $0\leq Alpha\leq 1$
 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 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]} .

ZOS

• The syntax is to calculate CONFIDENCE in ZOS 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 CONFIDENCE (Alpha,StandardDeviation,Size)} .
  • 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 Alpha} is value of the significance level.
• 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 Size} is the size of the sample.
• For e.g., CONFIDENCE(0.2,3.1,20)
• CONFIDENCE(0.67,8.3..10.3,51)

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

Related Videos

CONFIDENCE

See Also

• ZTEST
• ZTESTEQUALMEANS

References

CONFIDENCE

• List of Main Z Functions

• Z3 home