The document outlines the concepts of inferential statistics, focusing on parameter estimation and hypothesis testing. It explains the difference between null and alternative hypotheses, provides examples, and details the steps involved in hypothesis testing. Key statistical tests like p-value, t-test, and chi-square are mentioned as methods to evaluate these hypotheses.

1. INFERENTIAL STATISTICS
DR QURAT-UL-AIN
COMMUNITY DENTISTRY DEPARTMENT/ AIMI

2. LEARNING OBJECTIVES
•INFERENTIAL STATISTICS;
ESTIMATION OF PARAMETERS
HYPOTHESIS TESTING

3. INFERENTIAL STATISTIC
•The procedure followed in drawing
conclusion from the sample values are known
as statistic inference or inferential statistics.
•Consist of 2 aspects;
•ESTIMATION OF PARAMETERS
•HYPOTHESIS TESTING

4. PARAMETER ESTIMATION
•Parameter is any numerical quantity that
describes a certain population or some
characteristic of it.
•Tells us about the whole population
•Sample is used to estimate a parameter

5. Parameter & Statistic

6. WHAT IS A HYPOTHESIS
• Idea or Educated guess
• A statement that needs to be proved
• Should be testable, either by experiment or
observation.
• For example:
A new medicine you think might work.
More frequent intake of sugary drinks may lead to
multiple caries in children under 12 years of age.

7. TYPES OF HYPOTHESIS
1.Null Hypothesis (H0)
2.Alternative Hypothesis (Ha)

8. Null Hypothesis
It is denoted by H0
- Null hypothesis (H0) exists when a researcher believes there
is no relationship between the two variables, or there is a
lack of information to state a scientific hypothesis.
- Currently accepted value of a parameter (based on previous
studies established results)
- H0 nullifies/ rejected, the claim that the experimental result
is different from or better than one observed already.
- In other words, H0 states the observed difference is entirely
due to sampling error, that it has occurred purely by chance.
There is no significant change in my health
during the times when I drink green tea only or root beer
only.

9. Alternative Hypothesis
It is denoted by Ha
- Alternative hypothesis (Ha) of significant difference states that the
sample result is different that is, greater or smaller than the
hypothetical value of a population.
- Also called research hypothesis.
- It involves claim to be tested.
- Different test of significance such as p value, t-test, z-test, chi-square
test is performed to reject the Null hypothesis or failure to reject the
Null hypothesis.
- Example: My health improves during the times when I drink green
tea only, as opposed to root beer only.

10. • NULL:(H0) a statement that corresponds to the notion
that there is no association or difference between two
groups
• The null hypothesis is often an initial claim that
researchers specify using previous research or
knowledge.
• ALTERNATE:(H1) there is a difference or association
between two groups

11. Writing Null & Alternative Hypothesis
- Example 1:
Doctors believed that the average teenager sleeps on average no longer
than 8 hours per day. A researcher believes that teenager on average
sleeps longer.
- Null Hypothesis (H0) : µ ≤ 8 hours
- Alternative Hypothesis (Ha) : µ ˃ 8 hours
(where µ is the average number of hours teenager sleeps)

12. Writing Null & Alternative Hypothesis
- Example 2:
A healthcare provider saw that 48% of their patients received their flu shot in a recent
year. The healthcare provider tried a new advertising strategy in the following year,
and they took a sample of patients to test if the proportion who received their flu
shot had changed.
- Null Hypothesis (Ho) : p = 48%
- Alternative Hypothesis (Ha) : p ≠ 48%
(where p is the proportion of patients who received the flu shot)

13. HYPOTHESIS TESTING
• A statistical test used for deciding whether the
results of the sample data can be applied to the
entire population OR
• Used to decide whether there is enough
evidence in a sample of data to infer that a
certain condition is true for the entire
population.

14. Hypothesis Statement
•Include an “if” and “then”
•Include both the independent and dependent
variable
•Be testable
•Be based on prior research.

15. Steps in Hypothesis Testing
• Figure out your null hypothesis,
• State our null hypothesis
• Choose what kind of test you need to perform,
• Either support or reject the null hypothesis

16. Thank You For Listening
•ANY QUESTION?