Hypothesis Testing
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Hypothesis Testing
Descriptive Statistics -- show the sample results .
Inferential Statistics -- we want to generalize our results.
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Sampling becomes very important
 We must have probability samples
 Random sampling is best
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We set up a hypothesis:
 H0 The Null Hypothesis
 HA The Alternative Hypothesis
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Error Types
Decision based
on sample
Reject H0
Fail to reject H0
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Actual Value
H0 True
Type I error ()
1-
for Population
H0 False
1-
() Type II error
5
All the testing procedures we will discuss require us to set
Type I error (). The way we test then minimizes () Type
II error for all possible values of HA.
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Steps in Hypothesis Testing
1. H0 : State the Null hypothesis.
2. HA : State the Alternative hypothesis.
3. TSC :Calculated test statistic.
4. TSt : Tabulated value of the test statistic.
5. DR : Decision rule for rejecting H0.
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2)
Please evaluate the Virtual Adventures ride (Loch Ness Expedition)
(Please circle the appropriate answer).
Not At All
Very Much
Fun
1
2
3
4
5
Exciting
1
2
3
4
5
Challenging
1
2
3
4
5
Engaging Story
1
2
3
4
5
Unique Experience
1
2
3
4
5
Easy to Understand 1
2
3
4
5
Easy to Play
1
2
3
4
5
Family Fun
1
2
3
4
5
Total Enjoyment
1
2
3
4
5
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Code
8001
8002
Date
T
T
Session
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q1
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q2a
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q2b
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q2c
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q2d
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q2e
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q2f
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q2g
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q2h
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q2i
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8003
T
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8004
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8005
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8006
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8015
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One Sample Test of a Mean
Is the average Enjoyment Scale different from 4.09=36?
( X  )
t
s
n

X
s
n
t
prob
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36
35.98
5.02
209
-0.07
0.53
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One Sample Proportion
Is the true proportion of people who want to ride again .50?
ZC 
p
s
n
ZC
prob
*
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p *
 * (1   *)
n
0.93
0.03
209
12.52
<0.0001
0.50
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Test of Proportions: Two Independent Samples
Do men and women differ in the proportion who do not
want to ride again?
p* 
s
n1 p1  n2 p2
n1  n2
1 1
p * (1  p*)  
 n1 n2 
ZC 
p
n
p*
s
Z
prob
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p1  p2
s
Males
Females
0.0743
0.0492
148
61
0.0670
0.0014
17.3784
<0.0001
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“Do you think all positions would be the same fun level?”
by Position in VA.
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4) What control position did you play today? (Please circle the appropriate answer).
Commander
Pilot
Periscope Operator
Robotic Arm Operator
5) Before the game started, did you have any preferred position? (Check all that apply).
( ) Commander
( ) Pilot
( ) Periscope
( ) Robotic Arm
( ) No preference
If you played in a preferred position, please skip part b and go on to Question 6.
b) If you did not play in a preferred position, how much did being assigned to another
position affect you? (Please circle the appropriate answer).
Strongly negative
-5
-4
Strongly positive
-3
-2
-1
0
1
2
3
4
5
6) After having played Virtual Adventures, do you think all positions would be the same level of fun?
(Please circle the appropriate answer).
Yes
No
(If "No" please rank your preference for positions from "4" down to "1"
with "4" being most fun.)
(___) Commander
(___) Pilot
(___) Periscope
(___) Robotic Arm
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q4a
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q4b
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q5b
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q6
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q6a
q6b
q6c
q6d
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Test of Expectations:
More Than Two Independent Samples
“Do you think all positions would be the same fun level?”
by Position in VA.
(Oi  Ei )2
 
Ei
i 1
2
K
df  K  1
Count
of q6 q6
Position
0
1
2
3
4
Grand
Total
0
1
28 32
17 16
20 11
14 23
27 21
106 103
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Expectation
Grand
Under
Total Independence (O-E)^2/E
60 30.43 29.57 0.19 0.20
33 16.74 16.26 0.00 0.00
31 15.72 15.28 1.16 1.20
37 18.77 18.23 1.21 1.25
48 24.34 23.66 0.29 0.30
209
2
5.81 p=0.21
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Test of Means: Two Independent Samples
Does the mean Enjoyment Scale differ by gender?
HO : 1   2
H A : 1   2
X1  X2
s X1  X2
df  n1  n2  2
TSC : t 
TSt : t
(1
sX
1  X2

2

)
s12 s22

n1 n2
Gender
Data
Average of Enjoyment Scale
Var of Enjoyment Scale
Count of Gender
Difference
S
T
prob
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0-Male 1-Female
36.97
35.57
28.50
23.38
61
148
-1.40
0.79
-1.77
0.04
Grand
Total
35.98
25.15
209
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