1. Hypothesis Testing
GTECH 201
Lecture 16

2. Overview of Today’s Topic
Formulation
Evaluation
Refining and Restating
Statistical Tests

3. What is a Hypothesis? Unproven or unsubstantiated statement
You need to know the literature before you can formulate a hypothesis statement
Data collection should support hypothesis testing and evaluation
If hypothesis is tested and found to be correct, then results can be refined (different scenarios can be tested)
If partially correct, then hypothesis statement needs to be refined (reworded)

4. Hypothesis Testing
Multi-step procedure that leads the researcher from the hypothesis statement to the decision regarding the hypothesis
6- step process
State null and alternate hypotheses
Select appropriate statistical test
Select level of significance
Delineate regions of rejection and nonrejection of hypotheses
Calculate test statistic
Make regarding null hypothesis

5. Step 1 State null and alternate hypotheses Null hypothesis
A hypothesis to be tested
Usually represented as
Alternative hypothesis
A hypothesis considered as an alternate to the null hypothesis

6. Guidelines for Setting up H0, HA
Hypothesis tests concerning one parameter
Population mean, m
A null hypothesis for a hypothesis test concerning a population mean should always specify a single value for that parameter
(= ) sign must appear in the null hypothesis
Therefore:

7. Guidelines, part 2 Alternative hypothesis
The choice of the alternative hypothesis depends on and should reveal the purpose of the hypothesis test
Null hypothesis and alternative hypothesis are mutually exclusive
Three choices are possible

8. Guidelines, part 3
An alternate hypothesis with a sign is called a two-tailed test
The population mean, is different from a specified value,
When a < sign appears in the alternate hypothesis, the test is called a left-tailed test
When a > sign appears in the alternate hypothesis, the test is called a right-tailed test

9. Setting up Hypotheses
A snack food company produces 454 gms bags of pretzels. Although the actual weights deviate slightly from the 454 gms, and vary from one bag to another, the quality control team insists that the mean net weight of bags be maintained at 454 gms. If the mean net weight of the bags is lower or higher, it is likely to cause problems.
If you work for the quality control team and you want to decide whether the packaging machine is working properly, how would you set up a hypothesis test?

10. Stating Hypotheses The packaging machine IS working properly
The packaging machine IS NOT working properly

11. Select Appropriate Test
One sample difference of means t test
Objective
Compare a random sample mean to a population mean for difference
Requirements and assumptions
Random sample
Normally distributed population
Variable is measured at interval or ratio scale
Hypotheses
Test Statistic

12. Test Statistic sample mean population mean standard error of the mean
population standard deviation

13. Level of Significance  = 0.10 (90%); 0.05 (95%); 0.01 (99.7%) Errors
Type I error: Rejecting the null hypothesis when it is in fact true
Type II error: Not rejecting the null hypothesis when it is in fact false

14. Identify Regions of Rejection
Of null hypothesis
Two-tailed
Left tailed (directional)
Right tailed (directional)
Calculate test statistic
Make decision regarding null or alternate hypothesis

15. To Work in Class We want to investigate demographic change in an area
3500 households (HH)
You take a sample of 250 HH
Sample mean = 2.68; sample variance =4.3
 = 0.10 (90%)
Now, we want to find out if the mean HH size in this one area is typical or representative of the national mean household size (2.61)
Use the six step process to compare how closely the samples that you have taken compare with the national average HH size of 2.61

16. Limits of Hypothesis Testing
Pre-selecting level of significance
Lacks a theoretical basis
Used for convenience
Binary nature of null and alternative hypothesis
P-value or Probability value
Accepted approach
The exact significance level associated with the calculated test statistic is determined

17. More About P-Value We can define P-value as:
The exact probability of getting a test statistic value of a given magnitude, IF the null hypothesis is true
What is the probability of making a Type I error
Type I error occurs when the null hypothesis is rejected using the hypothesis testing procedure, even though in reality the null hypothesis is true

18. Comparing Classical and P Value Approaches
State hypotheses
Decide on significance level
Select test
Delineate regions of rejection/nonrejection
Calculate the test statistic
State your conclusion in words
P- Value
State hypotheses
Decide on significance level
Compute the value of the test statistic
Determine P-value
P reject null hypothesis; otherwise do not reject
State your conclusion in words

19. Guidelines for Using P-Value
Evidence against H0
Weak or none
Moderate
Strong
Very strong

20. Example
A random sample of 18 people with income below the poverty level reveals their daily intake of calcium
mean mg
standard deviation 188 mg
Use the P-value approach to determine whether the data provides sufficient evidence at the 5% significance level to conclude that the mean calcium intake of all Americans with income below the poverty level is less than the required daily allowance of 800 mg

21. Parametric and Nonparametric Tests
Require knowledge about population parameters
Assumptions made about population distribution
E.g., population is normally distributed
Sample data measured on Interval/Ratio scale
Non-parametric tests
Requires no knowledge about population parameters
Distribution-free
Some non-parametric tests are designed to be applied for nominal, ordinal data ( ) – we will talk about these in the next lecture

22. Choices/Options Run only a parametric test
Run only a non-parametric test
Run both tests
Goal
State the problem
Decide what inferential technique will be useful
Identify formulae associated with the technique
Interpret the results