80 Confidence Interval Critical Value

Confidence Interval Calculator

Utilize this calculator to compute the conviction interval or margin of error, assuming the sample mean nigh likely follows a normal distribution. Use the Standard Deviation Calculator if you accept raw data merely.

Sample size (amount), n
Sample Hateful (average), X̄
Standard Deviation, σ or s
Confidence Level

What is the confidence interval?

In statistics, a conviction interval is a range of values that is determined through the employ of observed data, calculated at a desired confidence level that may incorporate the true value of the parameter being studied. The confidence level, for example, a 95% confidence level, relates to how reliable the estimation procedure is, non the degree of certainty that the computed conviction interval contains the true value of the parameter beingness studied. The desired confidence level is chosen prior to the computation of the confidence interval and indicates the proportion of confidence intervals, that when constructed given the called confidence level over an space number of contained trials, will incorporate the true value of the parameter.

Confidence intervals are typically written as (some value) ± (a range). The range tin can exist written every bit an actual value or a percent. It can also be written every bit only the range of values. For example, the post-obit are all equivalent confidence intervals:

20.6 ±0.887

twenty.vi ±4.iii%

[19.713 – 21.487]

Calculating confidence intervals:

Calculating a confidence interval involves determining the sample hateful, X̄, and the population standard departure, σ, if possible. If the population standard deviation cannot exist used, then the sample standard deviation, due south, can be used when the sample size is greater than xxx. For a sample size greater than 30, the population standard deviation and the sample standard departure volition be similar. Depending on which standard divergence is known, the equation used to summate the confidence interval differs. For the purposes of this estimator, it is assumed that the population standard deviation is known or the sample size is larger plenty therefore the population standard deviation and sample standard departure is like. Only the equation for a known standard divergence is shown.

Where Z is the Z-value for the chosen confidence level, X̄ is the sample mean, σ is the standard deviation, and north is the sample size. Assuming the following with a confidence level of 95%:

10 = 22.8

Z = 1.960

σ = 2.7

north = 100

The confidence interval is:

22.8 ±0.5292

Z-values for Confidence Intervals