Confidence Interval Formula

About Confidence Interval Formula

In statistics, the confidence interval formula is used to express the level of uncertainty associated with a sample estimate of a population parameter. It's a term that describes the degree of uncertainty in a sampling procedure.

Remember that the confidence interval is a range in which the majority of potential values can be found. Set the confidence level to 90 per cent, 95 per cent, or 99 per cent, for example, to determine the confidence interval. At a 90% confidence level, we can expect the population parameter to appear in 90% of the interval estimates, 95% of the intervals, and so on.

What is Confidence Interval Formula?

A confidence interval specifies the range of possibilities for the parameter's true value. The investigator chooses the confidence level (in percentage). The confidence interval widens as the confidence level rises (less precise). The basic statistics formula and the z-score formula must be understood before learning the confidence interval. The confidence interval formula is shown below:

Confidence-interval formula:

Confidence Interval = x? ± Zc(σ / √ n), if n ≥ 30

Confidence Interval = x? ± Zc(S / √ n), if n < 30

Here,

n = Number of terms

x? = Sample Mean

σ = Standard Deviation

zc= In the z table, the value corresponds to the confidence interval.

tc= In the t table, the value corresponds to the confidence interval.

Solved examples of Confidence Interval Formula

Example 1:From a huge population, 30 apples were randomly selected. The sample had a mean diameter of 91 millimetres and a standard variation of 8 millimetres when measured. Calculate the 85 percent confidence intervals for the mean diameter of the entire apple population.

Sol:

For 85% confidence, Z = 1.440 We have x?:=91,s=8, Z=1.440 and n=30

Substitute into confidence interval formula:

x? ± z(S / √ n); Therefore, the 85%confidence limits are:
=91±1.440×8/√30
=91±1.440×8/5.477…
=91±2.1

Answer: The 85% confidence limits are=91±2.1

To get all the Maths formulas check out the main page. 

Pdf of Confidence Interval Formula

Confidence Interval Formula

Related Links

Frequently Asked Questions on Confidence Interval Formula