Confidence Level:

The confidence level describes the uncertainty associated with a sampling method.

Suppose we used the same sampling method (say sample mean) to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not.

**Constructing a Confidence Interval:**

Constructing a confidence interval involves 4 steps.

**Step 1**: Identify the sample problem. Choose the statistic (like sample mean, etc) that

you will use to estimate a population parameters.

**Step 2:** Select a confidence level. (Usually, it is 90%, 95% or 99%)

**Step 3**: Find the margin of error. (Usually given) If not given, use the following formula:-

Margin of error = Critical value * Standard deviation

**Step 4**: Specify the confidence interval. The uncertainty is denoted by the confidence level.

And the range of the confidence interval is defined by

where,

Sample_Statistic → Can be any kind of statistic. (eg. sample mean)

Margin_of_Error → generally, its (± 2.5)

Calculating a Confidence Interval

The calculation of CI requires two statistical parameters.

**Mean (μ)** — Arithmetic mean is the average of numbers. It is defined as the sum of n numbers divided by the count of numbers till n. (Eq-2)

μ = (1+2+3+…+n)/n

Standard deviation (σ) — It is the measure of how spread out the numbers are. It is defined as the summation of squared of the difference between each number and the mean. (Eq-3)

σ = √[Σ(xi - μ)^2/n]

**a) Using t-distribution**

We use t-distribution when the sample size n<30.

**b) Using a z-distribution**

We use z-distribution when the sample size n>30. Z-test is more useful when the standard deviation is known.