Za/2 For 86 Confidence Interval

Confidence Interval Reckoner

Use this computer to compute the conviction interval or margin of error, assuming the sample mean well-nigh likely follows a normal distribution. Use the Standard Deviation Computer if you accept raw data only.

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

What is the confidence interval?

In statistics, a confidence interval is a range of values that is determined through the use of observed data, calculated at a desired conviction level that may comprise the true value of the parameter being studied. The conviction level, for case, a 95% confidence level, relates to how reliable the interpretation procedure is, not the caste of certainty that the computed confidence interval contains the true value of the parameter being studied. The desired confidence level is chosen prior to the ciphering of the confidence interval and indicates the proportion of confidence intervals, that when constructed given the called confidence level over an infinite number of contained trials, volition contain the true value of the parameter.

Conviction intervals are typically written as (some value) ± (a range). The range can be written every bit an actual value or a per centum. Information technology can also be written every bit simply the range of values. For case, the following are all equivalent confidence intervals:

xx.6 ±0.887

20.vi ±iv.3%

[19.713 – 21.487]

Calculating conviction intervals:

Calculating a confidence interval involves determining the sample mean, X̄, and the population standard deviation, σ, if possible. If the population standard deviation cannot be used, then the sample standard deviation, s, can be used when the sample size is greater than thirty. For a sample size greater than 30, the population standard deviation and the sample standard deviation will exist similar. Depending on which standard deviation is known, the equation used to calculate the confidence interval differs. For the purposes of this calculator, it is causeless that the population standard divergence is known or the sample size is larger enough therefore the population standard deviation and sample standard divergence is similar. Merely the equation for a known standard departure is shown.

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

X = 22.eight

Z = 1.960

σ = 2.7

northward = 100

The confidence interval is:

22.8 ±0.5292

Z-values for Confidence Intervals

Confidence Level	Z Value
70%	one.036
75%	1.150
80%	1.282
85%	1.440
90%	1.645
95%	i.960
98%	2.326
99%	2.576
99.5%	ii.807
99.nine%	iii.291
99.99%	3.891
99.999%	4.417