A simple way to teach test of Hypothesis. Making it easier to learn.

1. Hypothesis Testing
Presented By:
Savi Arora

2. Hanging out with Sam. . .
• Let’s go for Bowling…
• Sam says, “My long term average is 150.”
• Over 3 games, Sam’s average score is 40.
• Do you believe him ?
• Is Sam a liar?

3. Is Sam a liar?
• Over 3 games, Sam’s average score is 40.
• Don’t believe him.
• Over 3 games, Sam’s average score is 140.
• More likely to believe him.
• At what point, between 40 and 140, do you make the decision to
believe Sam or not?

4. Is Sam a liar?
• What is your cut-off score for Sam?
• There is a “claim”, and if a sample outcome falls below a cut off value
(based on assumption that the claim is true)
• REJECT the claim.

5. Distribution of Bowling Score
Average bowling for 3 games
u = 150
Probabilities

6. Distribution of Bowling Score
Average bowling for 3 games
u = 150
Probabilities
c = 120
Rejection
region

7. Your Mum
• Lets go bowling with Your Mum.
• Your mum says, “Honey, my bowling average is 150.”
• Over 3 games, Your mum’s average score is 40.
• Tough Situation!

8. Distribution of Bowling Score
Average bowling for 3 games
u = 150
Probabilities
c = 70
Rejection
region

9. Hypothesis Testing
• Null Hypothesis (H0) is the “claim”
• ~ Sam claim that his bowling score average is 150
• Alternative Hypothesis (H1) is the counter-claim
• ~Sam’s bowling average is below 150; and he is a liar
• The Sample Statistics (X) is the observed sample estimate
• ~Sam’s bowling average for the 3 games you played together i.e. 40
• Critical Value (c) is the cut off value that indicated whether the claim is
rejected or not rejected.
• ~ You thought, if Sam score below 120, I’ll reject his claim
• Significance level (α) measure how sure you want to be when rejecting H0
• Small the α, the more sure you are when rejecting H0
• You’ll use a small significance level for your mum.

10. What is Hypothesis Testing?
• A statistical hypothesis is an assumption about a population
parameter.
• This assumption may or may not be true.
• Hypothesis testing refers to the formal procedures used by
statisticians to accept or reject statistical hypotheses.

11. Statistical Hypotheses
• The best way to determine whether a statistical hypothesis is true
would be to examine the entire population.
• But this is often impractical
• Examine a random sample from the population.
• If sample data are not consistent with the statistical hypothesis the
hypothesis is rejected.

12. Types of statistical hypotheses
• Null hypothesis. The null hypothesis, denoted by H0, is usually the
hypothesis that sample observations result purely from chance.
• Alternative hypothesis. The alternative hypothesis, denoted by H1 or
Ha, is the hypothesis that sample observations are influenced by some
non-random cause.

13. Example
• Suppose we wanted to determine whether a coin was fair and
balanced.
H0: P = 0.5
Ha: P ≠ 0.5
• Suppose we flipped the coin 50 times, resulting in 40 Heads and 10
Tails.
• Reject the Hypothesis?

14. Hypothesis Tests
1. State the hypotheses.
• Stating the null and alternative hypotheses.
• Mutually exclusive
2. Formulate an analysis plan.
• how to use sample data to evaluate the null hypothesis
3. Analyze sample data.
• Find the value of the test statistic
4. Interpret results.

15. Decision Errors
1. Type I error. A Type I error occurs when the researcher rejects a
null hypothesis when it is true.
The probability of committing a Type I error is called
the significance level,
also called alpha, denoted by α.
2. Type II error. A Type II error occurs when the researcher fails to
reject a null hypothesis that is false.

16. One tail vs Two tail
• specified that the population parameter lies entirely above or below
the value specified in H0 (one tailed)
H0: µ = 100 or H0: µ = 100
Ha: µ > 100 Ha: µ < 100
• specified that the parameter can lie on either side of the value
specified by H0 (two tailed)
H0: µ = 100 or H0: µ = 100
Ha: µ <> 100 Ha: µ ≠ 100

17. Thank You
Queries are Welcomed