Whenever we are going to predict a population parameter using sample data, it is always affected by some error. And this error is known as “**Margin of Error**”.

So the Interval Estimation can be expressed as:

Confidence Interval is dependent on:

**Sample Size:**More the sample size, lesser is the margin of error and narrower will be the confidence interval**Variability of Population:**More the Variability in population Data, more will be the standard deviation of population and more will be the Margin of Error**Confidence Level:**Higher the confidence level, wider will be the confidence interval

The 95% confidence level is the middle portion in the above figure and the leftover section on the left and right side is 5% combined which is 2.5% on each side.

Hence when we are referring to the **z-distribution table**, we need to look at the value 95 + 2.5 = 97.5 to get the critical value of 95%** confidence level**.

Look at the row and column value for the cell 0.975.

Row value is 1.9

Column value is 0.06

Hence **Critical value** will be 1.9 + 0.06 = 1.96 to get 95% confidence level

**Problem:**

We are given with the Standard Deviation of population weight to be 4 Kgs, and a sample of 100 people is chosen and their average weight is 62 kgs. What is the Standard Error, Margin of Error and Confidence interval for Confidence Level 95%?

Let us write what is given:

Standard Deviation of population = 4

Sample Size = 100

Sample Mean = 62

Confidence Level = 95

Standard Error = 4 / Square_root(100) = 4 / 10 = 0.4

For 95% confidence level, critical value is 1.96

Margin of Error = 1.96 x Standard Error

Margin of Error = 0.784

Confidence Interval = Sample mean +- Margin of Error

Lower bound of Confidence Interval = 62 - 0.784 = 61.216

Upper bound of Confidence Interval = 62 + 0.784 = 62.784

Hence the confidence interval will be [61.216, 62.784] with 95% of confidence level.

This means that there is 95% probability that the estimated confidence interval [61.216, 62.784] will contain the true population mean.

Courses | Blogs | Cheat Sheet | News Letter | About Us | Login | Contact | Privacy policy | Cookie policy

© Padhai Time 2022 | All Rights Reserved

We collect cookies and may share with 3rd party vendors for analytics, advertising and to enhance your experience. You can read more about our cookie policy by clicking on the 'Learn More' Button. By Clicking 'Accept', you agree to use our cookie technology.

Our Privacy policy can be found by clicking here