Confidence Interval

A range of values that we fairly sure the true value lies in. In statistical inference, to estimate the population parameters used the observed sample data.

Confidence interval also known as estimated range of values which include as unknown population parameter and the estimated range calculated from set of sample data (taken from Valerie J. Easton and John H. McColl's).

The confidence interval formula is

X  ±  Z	s
	√(n)

Where:

·         X is the mean

·         Z is the Z-value from the table below

·         s is the standard deviation

·         n is the number of samples

	Z
80%	1.282
85%	1.440
90%	1.645
95%	1.960
99%	2.576
99.5%	2.807
99.9%	3.291

Calculating the confidence interval

Step 1:

Note down all the number in the data, calculate the mean and standard deviation for the samples.

·         Number of samples: n = 40

·         Mean: X = 175

·         Standard Deviation: s = 20

Step 2:

Decide the confidence interval that we want. There are 90%, 95% and 99%. Then, find the value of "Z" for the confidence interval and let's say we choose 95%, the value of Z value is 1.960

	Z
80%	1.282
85%	1.440
90%	1.645
95%	1.960
99%	2.576
99.5%	2.807
99.9%	3.291

Step 3:

Insert the Z value into the formula and we have

175 ± 1.960 ×	20
	√40

The result is 

175cm ± 6.20cm

In conclusion, the data lies between 168.8cm to 181.2cm

By: Nur Fariza

References:

Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

https://www.mathsisfun.com/data/confidence-interval.html

http://www.stat.yale.edu/Courses/1997-98/101/confint.htm