The document discusses the concepts of statistics and probability, emphasizing the importance of estimates and confidence intervals in data analysis. It explains that a confidence interval helps to quantify uncertainty about population parameters, with larger sample sizes yielding smaller intervals. Additionally, it provides formulas and examples for calculating the length of confidence intervals.

1. STATISTICS AND
PROBABILITY
MODULE 4: LENGTH OF CONFIDENCE INTERVAL

2. STATISTICS AND PROBABILITY
◦Probability And Statistics are the two important
concepts in Maths. Probability is all about
chance. Whereas statistics is more about how we
handle various data using different techniques. It
helps to represent complicated data in a very
easy and understandable way.

3. DELETE!
◦ Before we understand the confidence Interval, let us first
understand what do we mean by “Estimate“. Everyone makes
some kinds of estimates at some point of time in their life. Imagine
that you are crossing the road, and you see the car that is
approaching you fast and now you can estimate the speed of that
same car that is approaching you. Based on this estimate you can
make your decision if you to wait, walk or run. This is
called Estimate.

4. Question!
◦ How do you understand confidence level and sample size?
◦ The larger your sample, the more sure you can be that their answers truly reflect the population. This
indicates that for a given confidence level, the larger your sample size, the smaller your confidence interval.
◦ .

5. LENGTH OF CONFIDENCE
INTERVAL
◦CONFIDENCE INTERVAL- In statistics, this refers to the
probability that a Population parameter will fall between a set
of values for a certain proportion of times. Confidence
intervals measure the degree of uncertainty or certainty in a
sampling method. They can take any number of probability
limits, with the most common being a 95% or 99%
confidence level.

6. CONFIDENCE INTERVAL

7. NARROWNESS OF THE INTERVAL
◦This pertains to a small width in
relation to the length of the
confidence interval.

8. EXAMPLE

9. FORMULA
Where: LCI = |UCL – LCL| = |LCL – UCL|
Or
LCI = UCL – LCL
LCI – length of confidence interval
UCL – upper confidence limit
LCL – lower confidence limit

10. EXAMPLE
◦Example 1. Find the length of the confidence
interval 0. 275<p<0.360
◦Example 2. Find the length of the confidence
interval upper confidence limit = 0.805 lower
confidence limit = 0.526

11. WORKSHEET 1

12. STATISTICS AND
PROBABILITY
APPROPRIATE SAMPLE SIZE

14. EXAMPLE

17. EXAMPLE