1. Hypothesis Testing Make a tentative assumption about a parameter
Evaluate how likely we think this assumption is true
Null Hypothesis
Default possibility
H0:  = 13
H0:  = 0
Alternative (or Research) Hypothesis
Values of a parameter if your theory is correct
HA:  > 13
HA:   0

2. Hypothesis Testing _ _ Test Statistic
Measure used to assess the validity of the null hypothesis
Rejection Region
A range of values such that if our test statistic falls into this range, we reject the null hypothesis
H0:  = 13
If x is close to 13, can’t reject H0. But if x is far away, then reject. But what’s “far away” ?? _ _

3. Hypothesis Testing Errors
State of Nature (Truth)
H0 True
H0 False
Reject H0
Fail to
Action

4. Hypothesis Testing Errors
Drug Testing Example
H0: Not using drugs
State of Nature (Truth)
H0 True
H0 False
Reject H0
Conclude
“a drug user”
Fail to Reject H0
“clean”
Action

5. Testing 
A human resources executive for a huge company wants to set-up a self-insured workers’ compensation plan based on a company-wide average of 2,000 person-days lost per plant. A survey of 51 plants in the company reveals that x = 1,800 and s = 500. Is there sufficient evidence to conclude that company-wide days lost differs from 2,000? (Use  = 0.05) _

6. If H0 is true… _ x has a t distribution with 50 degrees of freedom
2,000 _

7. P(rejection region) = 
When to Reject H0? _
x has a t distribution with 50 degrees of freedom
Rejection Region
P(rejection region) =  _ _
x =
2,000 _ xL
xUP

8. Testing 
Suppose you are a human resources manager and are investigating health insurance costs for your employees. You know that five years ago, the average weekly premium was $ You take a random sample of 40 of your employees and calculate that x = $31.25 and s = 5.
Have health care costs increased (use a 5% significance level)? _

9. If H0 is true… _ x has a t distribution with 39 degrees of freedom30 _

10. P(rejection region) = 
When to Reject H0? _
x has a t distribution with 39 degrees of freedom
P(rejection region) = 
Rejection Region _
x = 30 _
xUP

11. t Values for 39 d.f. x P(t<x) 1.55 0.9354 1.56 0.9366 1.57 0.9378
1.58
0.9389
1.59
0.9400
1.60
0.9412

12. Important Note
Siegel emphasizes confidence intervals to do hypothesis tests
I do NOT want you to do it this way
It does not fit the logic that I will emphasize
It doesn’t fit with p-values
It’s too easy to get confused between one-tailed and two-tailed tests
So don’t follow Siegel, follow Budd

13. Testing p
An HR manager of a large corporation surveys 1,000 workers and asks “Are you satisfied with your job?” The results are
Responses Percentage
Satisfied %
Not Satisfied %
You want to examine whether dissatisfaction is increasing. You know that the fraction of workers who were dissatisfied with their job five years ago was 20%. Has the fraction increased (at the 5% significance level)?

14. Regression Recall Coal Mining Safety Problem
Dependent Variable: annual fatal injuries
injury = hours tons
(258.82) (0.186) (0.403)
unemp WWII
(5.660) (78.218)
Act Act1969
( ) ( )
(R2 = , n=47)
Test the hypothesis that the unemployment rate is not related to the injury rate (use =0.01)

15. Regression Statistics
Excel Output
Regression Statistics
R Squared
0.955
Adj. R Squared
0.949
Standard Error
Obs. 47
ANOVA df SS MS F
Significance
Regression 6
0.000
Residual 40
Total 46
Coeff.
Std. Error
t stat
p value
Lower 95%
Upper 95%
Intercept
-0.651
0.519
hours
1.244
0.186
6.565
0.001
0.002
tons
0.048
0.403
0.119
0.906
-0.001
unemp
19.618
5.660
3.466
8.178
31.058
WWII
78.218
2.044
1.766
Act1952
-9.839
-0.098
0.922
Act1969
-1.820
0.076
22.411

16. Minitab Output Predictor Coef StDev T P
Constant
hours
tons
unemp
WWII
1952Act
1969Act
S = R-Sq = 95.5% R-Sq(adj) = 94.9%

17. Testing 1- 2
To compare wages in two large industries, we draw a random sample of 46 hourly wage earners from each industry and find x1 = $7.50 and x2 = $7.90 with s1 = 2.00 and s2 = 1.80.
Is there sufficient evidence to conclude (using  = 0.01) that the average hourly wage in industry 2 is greater than the average in industry 1? _ _

18. Testing p1- p2
In a random survey of 850 companies in 1995, 73% of the companies reported that there were no difficulties with employee acceptance of job transfers. In a random survey of 850 companies in 1990, the analogous proportion was 67%. Do these data provide sufficient evidence to conclude that the proportion of companies with no difficulties with employee acceptance of job transfers has changed between 1990 and 1995? (Use  = 0.05) _

19. Many Cases, Same Logic
If you get a “small” test statistic, then there is a decent probability that you could have drawn this sample with H0 true—so not enough evidence to reject H0
If you get a “large” test statistic, then there is a low probability that you could have drawn this sample with H0 true—the safe bet is that H0 is false
Need the t or z distribution to distinguish “small” from “large” via probability of occurrence

20. More Exercises
A personnel department has developed an aptitude test for a type of semiskilled worker. The test scores are normally distributed. The developer of the test claims that the mean score is 100. You give the test to 36 semiskilled workers and find that x = 98 and s = 5. Do you agree that µ = 100 at the 5% level?
Have 50% of all Cyberland Enterprises employees completed a training program? Recall that for the Cyberland Enterprises sample, 29 of the 50 employees sampled completed a training program. (Use  = 0.05) _

21. More Exercises Dep. Var: Job Performance n=3525 Use =0.01
Predictor Coef StDev T P
Constant
age
seniorty
cognitve
strucint
manual
Manl*age
On average, is performance related to seniority?
Do those with structured interviews have higher average performance levels than those without?
Do those with structured interviews have higher average performance levels at least two units greater than those without?
Does the relationship between age and performance differ between manual and non-manual jobs?
Dep. Var: Job Performance
n=3525
Use =0.01

22. More Exercises
A large company is analyzing the use of its Employee Assistance Program (EAP). In a random sample of 500 employees, it finds:
Single Employees Married Employees
number of employees
number using the EAP
Using =0.01, is there sufficient evidence to conclude that single and married employees differ in the usage rate of the EAP?

23. More Exercises
Independent random samples of male and female hourly wage employees yield the following summary statistics:
Male Employees Female Employees
n1 = n2 = 32
x1 = x2 = 8.70
s1 = s2 = 0.80
Is there sufficient evidence to conclude that, on average, women earn less than men? (Use  = 0.10) _ _