Tech Notes

My notes on Statistics, Big Data, Cloud Computing, Cyber Security

Confidence Interval and Level

Confidence Interval

The purpose of taking a random sample from a lot or population and computing a statistic, such as the mean from the data, is to approximate the mean of the population. How well the sample statistic estimates the underlying population value is always an issue. A confidence interval addresses this issue because it provides a range of values which is likely to contain the population parameter of interest.

Confidence Level

Confidence intervals are constructed at a confidence level, such as 95%, selected by the user. What does this mean? It means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.

It represents the likelihood that another sample will provide the same results

Relationship Between the Confidence Level & Confidence Interval

“We are 95% confident that results of the telephone poll indicate a result of 19 out of 20 with a margin of error of 3%”

Here 95% is the confidence level and confidence interval is (-3% < result < 3%)

How to calculate Confidence Interval

  1. Note the Hypothesis being tested. Eg. The average weight of a male student in ABC University is 180 kgs
  2. Select a sample from the chosen population. Eg Randomly select 1,000 male students.
  3. Calculate sample mean and sample standard deviation. Choose a sample statistic (e.g., sample mean, sample standard deviation) that can be used to estimate your chosen population parameter. A population parameter is a value that represents a particular population characteristic
  4. Choose desired confidence level. Eg 95%
  5. Calculate your margin of error = Critical Value * Standard Error10.12 where ß is the sample proportion, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (from the following table).
    z*-Values for Selected (Percentage) Confidence Levels
    Percentage Confidence z*-Value
    80 1.28
    90 1.645
    95 1.96
    98 2.33
    99 2.58
  6. Confidence Interval = Sample Statistic +/- margin of error

Another representation

Screenshot_112213_051748_PM

Screenshot_112213_053856_PM

Disclaimer : These are my study notes – online – instead of on paper so that others can benefit. In the process I’ve have used some pictures / content from other original authors. All sources / original content publishers are listed below and they deserve credit for their work. No copyright violation intended.

References for these notes :

http://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm

http://www.dummies.com/how-to/content/how-to-calculate-the-margin-of-error-for-a-sample0.html

http://www.wikihow.com/Calculate-Confidence-Interval

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: