ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
17
17
18
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Gender
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
Major
Finance
Finance
Leadership
Finance
Finance
Marketing
Marketing
Leadership
Leadership
Finance
No Major
No Major
Finance
Finance
Finance
Leadership
Finance
No Major
Finance
Leadership
Leadership
Finance
Leadership
Finance
Leadership
Finance
Leadership
Leadership
Leadership
Leadership
Leadership
Marketing
Finance
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Finance
Leadership
Leadership
Finance
Leadership
Finance
Employ
Full Time
Full Time
Unemployed
Part Time
Full Time
Full Time
Full Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Part Time
Full Time
Part Time
Full Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Part Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Age
26
32
26
37
43
47
32
41
56
46
36
29
36
37
50
56
52
58
40
31
33
37
30
42
30
43
31
32
35
45
48
33
45
38
47
48
43
44
44
49
44
45
49
47
49
MBA_GPA
3,95
3,45
3,30
3,55
3,35
3,75
3,50
3,60
3,65
3,80
3,35
3,70
3,35
3,05
3,30
3,65
3,15
3,10
3,80
3,60
3,15
3,70
3,30
3,70
3,85
3,75
3,35
3,30
3,85
3,15
3,70
3,05
3,10
3,30
3,05
3,45
3,85
3,90
3,92
3,85
3,85
3,75
3,10
3,95
3,25
BS GPA Hrs_Studying
10
3,45
8
3,39
7
3,63
8
3,48
7
3,52
9
3,81
10
3,45
8
3,66
8
3,74
9
3,87
7
3,68
9
3,75
7
3,62
4
3,07
7
3,54
8
3,75
7
3,31
6
3,2
9
3,11
8
3,84
7
3,39
8
3,74
7
3,44
8
3,94
9
3,96
11
3,75
7
3,28
7
3,45
9
3,34
7
3,44
9
3,86
4
3,07
6
3,16
7
3,39
2
3,02
8
3,65
9
3,88
11
3,56
11
3,37
9
3,77
9
3,89
9
3,89
6
3,13
10
4
7
3,38
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Leadership
Marketing
No Major
Leadership
Leadership
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Leadership
Marketing
Leadership
Marketing
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Finance
Leadership
Marketing
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
48
52
59
29
49
49
52
45
47
52
30
27
38
33
37
27
29
44
53
50
46
47
33
34
35
47
48
48
35
35
36
37
50
41
53
43
55
58
61
34
44
29
45
45
32
42
32
3,60
3,60
3,10
3,35
3,96
3,65
3,90
3,40
3,40
3,10
3,80
3,60
3,74
3,10
3,65
3,40
3,85
3,20
3,15
3,97
3,80
3,10
3,93
3,91
3,70
3,05
3,75
3,80
3,95
3,65
3,90
3,45
3,80
3,80
3,55
3,80
3,45
3,80
3,45
3,90
3,65
3,95
3,60
3,85
3,50
3,40
3,60
3,63
3,66
3,21
3,38
3,65
3,87
3,88
3,7
3,66
3,19
3,87
3,56
3,44
3,14
3,66
3,68
3,91
3,43
3,23
3,01
3,81
3,11
3,76
3,84
3,78
3,13
3,69
3,86
3,65
3,92
3,87
3,77
3,87
3,78
3,75
3,93
3,71
3,95
3,58
3,97
3,81
3,99
3,6
3,93
3,6
3,43
3,78
8
11
6
7
11
8
9
8
8
6
9
11
10
6
8
8
9
7
7
11
9
5
11
10
9
5
9
9
10
8
9
8
9
9
8
9
8
9
8
11
8
10
8
9
8
8
8
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
120
121
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
Marketing
Marketing
No Major
No Major
No Major
Marketing
Marketing
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
No Major
Marketing
Marketing
Marketing
No Major
Finance
Finance
No Major
No Major
No Major
No Major
Marketing
No Major
No Major
No Major
No Major
No Major
No Major
No Major
No Major
No Major
Marketing
Finance
Finance
Finance
Finance
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Part Time
Part Time
34
34
30
26
26
39
44
50
52
52
30
34
30
53
52
54
56
57
57
59
59
30
37
48
37
33
47
35
30
42
42
43
53
50
50
47
48
48
53
53
55
56
38
30
34
42
28
3,50
3,95
3,10
3,20
3,15
3,05
3,55
3,70
3,55
3,95
3,15
3,55
3,50
3,75
3,15
3,15
3,40
3,20
3,40
3,65
3,75
3,20
3,30
3,85
3,30
3,30
3,85
3,25
3,85
3,60
3,95
3,95
3,98
3,25
3,50
3,75
3,45
3,65
3,30
3,90
3,35
3,55
3,05
3,65
3,75
3,05
3,95
3,79
3,61
3,19
3,42
3,24
3,03
3,86
3,69
3,76
4
3,35
3,66
3,57
3,97
3,25
3,26
3,61
3,37
3,48
3,87
3,78
3,49
3,48
3,97
3,46
3,4
3,6
3,26
3,88
3,87
3,92
3,93
3,94
3,36
3,78
3,9
3,53
3,78
3,24
3,96
3,66
3,47
3,04
3,86
3,98
3,05
3,23
8
10
6
7
6
2
9
9
8
10
7
8
8
9
6
7
8
7
8
8
9
7
7
9
7
7
9
7
9
8
10
10
10
7
8
9
8
8
7
9
7
8
4
8
9
5
10
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
Finance
Finance
Finance
Finance
Finance
Finance
Finance
Finance
Leadership
Leadership
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Leadership
Leadership
Leadership
Leadership
Finance
Finance
Leadership
Finance
Leadership
Leadership
Leadership
Marketing
Finance
Finance
No Major
No Major
No Major
No Major
Finance
Finance
Finance
Marketing
Marketing
Marketing
Marketing
Marketing
Leadership
No Major
No Major
Finance
Leadership
Part Time
Part Time
Part Time
Part Time
Part Time
Full Time
Full Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Full Time
Full Time
Part Time
Full Time
Full Time
Full Time
Part Time
Part Time
Full Time
Full Time
Part Time
Part Time
Part Time
Part Time
Unemployed
Unemployed
Unemployed
Part Time
Part Time
Part Time
Part Time
Part Time
Unemployed
Part Time
Part Time
Unemployed
Unemployed
43
45
46
46
46
41
42
48
42
34
48
53
53
31
34
34
36
52
53
53
45
34
44
44
36
36
52
37
48
49
37
43
54
56
30
43
47
27
34
36
37
45
54
31
38
31
51
3,50
3,40
3,20
3,90
3,55
3,90
3,75
3,90
3,55
3,25
3,25
3,20
3,95
3,20
3,80
3,35
3,60
3,50
3,50
3,40
3,20
3,60
3,45
3,05
3,74
3,25
3,45
3,05
3,70
3,90
3,45
3,90
3,50
3,40
3,20
3,25
3,15
3,70
3,95
3,45
3,35
3,55
3,05
3,75
3,35
3,25
3,25
3,5
3,27
3,35
3,84
3,86
3,92
3,73
3,84
3,55
3,45
3,25
3,23
3,85
3,44
3,98
3,27
3,75
3,44
3,48
3,62
3,44
3,81
3,78
3,05
3,68
3,43
3,59
3,06
3,87
3,81
3,53
3,99
3,39
3,55
3,33
3,25
3,28
3,78
2,92
3,54
3,68
3,49
3,09
3,88
3,69
3,39
3,31
8
8
7
9
8
9
9
9
8
7
7
7
10
7
11
7
8
8
10
8
7
8
8
4
10
7
8
4
9
9
8
9
8
8
7
7
7
11
10
8
7
8
5
9
7
7
7
187
188
189
190
191
192
193
194
195
196
197
198
199
200
0
0
0
0
0
0
0
0
0
0
0
1
0
1
Finance
Finance
Marketing
No Major
Finance
Leadership
Marketing
Marketing
Marketing
Leadership
Marketing
No Major
Marketing
No Major
Unemployed
Unemployed
Unemployed
Full Time
Part Time
Unemployed
Unemployed
Full Time
Full Time
Unemployed
Unemployed
Unemployed
Unemployed
Unemployed
36
40
45
59
27
49
32
30
31
55
27
54
42
30
3,55
3,20
3,15
3,65
3,50
3,40
3,70
3,94
3,70
3,30
3,35
3,10
3,25
3,10
3,71
3,44
3,29
3,86
3,65
3,28
3,89
3,21
3,83
3,54
3,58
3,18
3,42
3,15
8
7
7
8
8
8
9
11
9
7
7
5
7
6
Works FT
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
Variable descriptions
Gender = 0 (female), 1 (male)
Major = student's major
Age = age of student in years
MBA_GPA = overall GPA in the MBA program
BS_GPA = overall GPA in the BS program
Hrs_Studying = average hours studied per week
Works FT = 0 (No), 1 (Yes)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
Unit 4
Practice Problems
Practice Problem One
Two Sample Hypothesis Test for the Mean (Independent Samples)
Level of Significance
0.05
Sample Mean
Sample Size
Sample Standard Deviation
No Pool
202763.158
38
33716.973
Standard Error (Computed)
Test Statistic (Computed)
8037.41
-2.80
Pool
225258.065
62
46371.959
This is a two-tailed test since we are testing if the mean is different for the houses with vs. without a pool.
The p-value of .0062 is less than .05, and so we reject the null hypothesis and conclude that the mean
sales price for homes is different for houses with vs. without a pool. The fact that the sample mean is
greater for houses with a pool indicates that houses with a pool likely have a higher mean price in the
population.
Two-Tailed Test
( )
Lower
Upper
Crit Value
Crit Value
-1.9600
1.9600
pValue
Decision
0.0062
Reject the null hypothesis
Home Prices with and without Pool
$230,000.00
$225,000.00
$220,000.00
$215,000.00
$210,000.00
$205,000.00
$200,000.00
$195,000.00
$190,000.00
No Pool
Pool
Unit 4
Practice Problems
Practice Problem Two
Two Sample Hypothesis Test for the Mean (Paired Samples)
Level of Significance
0.05
Standard Error (Computed)
Test Statistic (Computed)
3442.16
0.29
This is a two-tailed test since we are testing whether the mean appraisals given by the two agents are
different from one another. The p-value of 0.7720 is greater than .05, and so we fail to reject the null
hypothesis; there is insufficient evidence to conclude the mean appraisals are different for the two agents.
As a result we conclude that the two agents’ appraisals are not significantly different from one another.
Two-Tailed Test
Lower
Crit Value
Upper
Crit Value
p-Value
Decision
-1.9842
1.9842
0.7720
Do not reject the null
hypothesis
(d ) ( )
Comparison of Two Agents' Appraisals
$350,000
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
$0
1
11
21
31
41
Agent 1
51
61
Agent 2
71
81
91
Unit 4
Practice Problems
Practice Problem Three
Two Sample Hypothesis Test for the Proportion
Level of Significance
0.05
Number of Successes
Sample Size
Brick
30
40
Wood or Stucco
32
60
Proportion (Computed)
0.75
0.53
Z Test Statistic
(Computed)
2.19
This is an upper-tailed test since we are testing whether the proportion for brick homes with a pool is
greater than that of wood & stucco homes with a pool. The p-value of .0144 is less than .05, and so we
reject the null hypothesis. As a result, we conclude that brick homes are more likely to have a swimming
pool than wood & stucco homes.
Upper-Tail Test
H1: (P1 > P2 or P2 < P1)
Lower Crit
Value
Upper Crit
Value
pValue
Decision
n/a
1.6449
0.0144
Reject the null hypothesis
Relationship between Construction Type and Pools
100%
80%
Without Pool
60%
With Pool
40%
20%
0%
Brick
Wood or Stucco
Unit 4
Practice Problems
Practice Problem Four
Analysis of Variance
SUMMARY
Groups
2 BR
3 BR
4 BR
5 BR
Count
24
26
26
24
Sum
4807000.000
5574000.000
5552000.000
5738000.000
ANOVA
Source of Variation
Treatment
Error
SS
18885182948.718
166271407051.282
df
3
96
Total
185156590000.000
99
Average
200291.667
214384.615
213538.462
239083.333
MS
6295060982.906
1731993823.451
Variance
1904911231.884
1205046153.846
1457058461.538
2430688405.797
F
3.635
F crit
2.699
The p-value of .0156 is less than .05, and so we reject the null hypothesis. Thus we conclude that a
difference exists in the mean sales price based on number of bedrooms that a home has. Looking at the
Post Hoc tests, we see that homes with 5 bedrooms are worth significantly more than homes with 2, 3 or
4 bedrooms. There doesn't appear to be a significant difference in mean prices for homes with 2, 3 or 4
bedrooms.
Null hypothesis:
Alternate hypothesis:
Significance level:
p-Value
Decision:
= = =
Not all the means are equal
0.05
0.0156
Reject the null hypothesis
Mean Differences Post-Hoc Tests
Difference
Comparison
of Means
2 BR to 3 BR
2 BR to 4 BR
3 BR to 4 BR
2 BR to 5 BR
3 BR to 5 BR
4 BR to 5 BR
14092.949
13246.795
846.154
38791.667
24698.718
25544.872
Lower
Conf. Limit
-9291.274
-10137.428
-22065.612
14944.345
1314.495
2160.649
Upper
Conf. Limit
37477.172
36631.018
23757.920
62638.989
48082.941
48929.095
Difference in
Treatment
Means???
- no difference - no difference - no difference ***Means are different***
***Means are different***
***Means are different***
Unit 4
Practice Problems
Practice Problem Four (continued)
Comparison of Number of Bedrooms and
Home Price
$240,000
$230,000
$220,000
$210,000
$200,000
$190,000
$180,000
2 BR
3 BR
4 BR
5 BR
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
17
17
18
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Gender
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
Major
Finance
Finance
Leadership
Finance
Finance
Marketing
Marketing
Leadership
Leadership
Finance
No Major
No Major
Finance
Finance
Finance
Leadership
Finance
No Major
Finance
Leadership
Leadership
Finance
Leadership
Finance
Leadership
Finance
Leadership
Leadership
Leadership
Leadership
Leadership
Marketing
Finance
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Finance
Leadership
Leadership
Finance
Leadership
Finance
Employ
Full Time
Full Time
Unemployed
Part Time
Full Time
Full Time
Full Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Part Time
Full Time
Part Time
Full Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Part Time
Part Time
Part Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Age
26
32
26
37
43
47
32
41
56
46
36
29
36
37
50
56
52
58
40
31
33
37
30
42
30
43
31
32
35
45
48
33
45
38
47
48
43
44
44
49
44
45
49
47
49
MBA_GPA
3.95
3.45
3.30
3.55
3.35
3.75
3.50
3.60
3.65
3.80
3.35
3.70
3.35
3.05
3.30
3.65
3.15
3.10
3.80
3.60
3.15
3.70
3.30
3.70
3.85
3.75
3.35
3.30
3.85
3.15
3.70
3.05
3.10
3.30
3.05
3.45
3.85
3.90
3.92
3.85
3.85
3.75
3.10
3.95
3.25
BS GPA Hrs_Studying
10
3.45
8
3.39
7
3.63
8
3.48
7
3.52
9
3.81
10
3.45
8
3.66
8
3.74
9
3.87
7
3.68
9
3.75
7
3.62
4
3.07
7
3.54
8
3.75
7
3.31
6
3.2
9
3.11
8
3.84
7
3.39
8
3.74
7
3.44
8
3.94
9
3.96
11
3.75
7
3.28
7
3.45
9
3.34
7
3.44
9
3.86
4
3.07
6
3.16
7
3.39
2
3.02
8
3.65
9
3.88
11
3.56
11
3.37
9
3.77
9
3.89
9
3.89
6
3.13
10
4
7
3.38
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Leadership
Marketing
No Major
Leadership
Leadership
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Leadership
Marketing
Leadership
Marketing
Leadership
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Finance
Leadership
Marketing
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
48
52
59
29
49
49
52
45
47
52
30
27
38
33
37
27
29
44
53
50
46
47
33
34
35
47
48
48
35
35
36
37
50
41
53
43
55
58
61
34
44
29
45
45
32
42
32
3.60
3.60
3.10
3.35
3.96
3.65
3.90
3.40
3.40
3.10
3.80
3.60
3.74
3.10
3.65
3.40
3.85
3.20
3.15
3.97
3.80
3.10
3.93
3.91
3.70
3.05
3.75
3.80
3.95
3.65
3.90
3.45
3.80
3.80
3.55
3.80
3.45
3.80
3.45
3.90
3.65
3.95
3.60
3.85
3.50
3.40
3.60
3.63
3.66
3.21
3.38
3.65
3.87
3.88
3.7
3.66
3.19
3.87
3.56
3.44
3.14
3.66
3.68
3.91
3.43
3.23
3.01
3.81
3.11
3.76
3.84
3.78
3.13
3.69
3.86
3.65
3.92
3.87
3.77
3.87
3.78
3.75
3.93
3.71
3.95
3.58
3.97
3.81
3.99
3.6
3.93
3.6
3.43
3.78
8
11
6
7
11
8
9
8
8
6
9
11
10
6
8
8
9
7
7
11
9
5
11
10
9
5
9
9
10
8
9
8
9
9
8
9
8
9
8
11
8
10
8
9
8
8
8
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
120
121
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
Marketing
Marketing
No Major
No Major
No Major
Marketing
Marketing
Marketing
Marketing
Marketing
Leadership
Leadership
Leadership
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
Marketing
No Major
Marketing
Marketing
Marketing
No Major
Finance
Finance
No Major
No Major
No Major
No Major
Marketing
No Major
No Major
No Major
No Major
No Major
No Major
No Major
No Major
No Major
Marketing
Finance
Finance
Finance
Finance
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Full Time
Unemployed
Full Time
Full Time
Part Time
Part Time
34
34
30
26
26
39
44
50
52
52
30
34
30
53
52
54
56
57
57
59
59
30
37
48
37
33
47
35
30
42
42
43
53
50
50
47
48
48
53
53
55
56
38
30
34
42
28
3.50
3.95
3.10
3.20
3.15
3.05
3.55
3.70
3.55
3.95
3.15
3.55
3.50
3.75
3.15
3.15
3.40
3.20
3.40
3.65
3.75
3.20
3.30
3.85
3.30
3.30
3.85
3.25
3.85
3.60
3.95
3.95
3.98
3.25
3.50
3.75
3.45
3.65
3.30
3.90
3.35
3.55
3.05
3.65
3.75
3.05
3.95
3.79
3.61
3.19
3.42
3.24
3.03
3.86
3.69
3.76
4
3.35
3.66
3.57
3.97
3.25
3.26
3.61
3.37
3.48
3.87
3.78
3.49
3.48
3.97
3.46
3.4
3.6
3.26
3.88
3.87
3.92
3.93
3.94
3.36
3.78
3.9
3.53
3.78
3.24
3.96
3.66
3.47
3.04
3.86
3.98
3.05
3.23
8
10
6
7
6
2
9
9
8
10
7
8
8
9
6
7
8
7
8
8
9
7
7
9
7
7
9
7
9
8
10
10
10
7
8
9
8
8
7
9
7
8
4
8
9
5
10
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
Finance
Finance
Finance
Finance
Finance
Finance
Finance
Finance
Leadership
Leadership
Leadership
Finance
Finance
Leadership
Leadership
Leadership
Leadership
Leadership
Leadership
Leadership
Finance
Finance
Leadership
Finance
Leadership
Leadership
Leadership
Marketing
Finance
Finance
No Major
No Major
No Major
No Major
Finance
Finance
Finance
Marketing
Marketing
Marketing
Marketing
Marketing
Leadership
No Major
No Major
Finance
Leadership
Part Time
Part Time
Part Time
Part Time
Part Time
Full Time
Full Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Part Time
Full Time
Full Time
Part Time
Full Time
Full Time
Full Time
Part Time
Part Time
Full Time
Full Time
Part Time
Part Time
Part Time
Part Time
Unemployed
Unemployed
Unemployed
Part Time
Part Time
Part Time
Part Time
Part Time
Unemployed
Part Time
Part Time
Unemployed
Unemployed
43
45
46
46
46
41
42
48
42
34
48
53
53
31
34
34
36
52
53
53
45
34
44
44
36
36
52
37
48
49
37
43
54
56
30
43
47
27
34
36
37
45
54
31
38
31
51
3.50
3.40
3.20
3.90
3.55
3.90
3.75
3.90
3.55
3.25
3.25
3.20
3.95
3.20
3.80
3.35
3.60
3.50
3.50
3.40
3.20
3.60
3.45
3.05
3.74
3.25
3.45
3.05
3.70
3.90
3.45
3.90
3.50
3.40
3.20
3.25
3.15
3.70
3.95
3.45
3.35
3.55
3.05
3.75
3.35
3.25
3.25
3.5
3.27
3.35
3.84
3.86
3.92
3.73
3.84
3.55
3.45
3.25
3.23
3.85
3.44
3.98
3.27
3.75
3.44
3.48
3.62
3.44
3.81
3.78
3.05
3.68
3.43
3.59
3.06
3.87
3.81
3.53
3.99
3.39
3.55
3.33
3.25
3.28
3.78
2.92
3.54
3.68
3.49
3.09
3.88
3.69
3.39
3.31
8
8
7
9
8
9
9
9
8
7
7
7
10
7
11
7
8
8
10
8
7
8
8
4
10
7
8
4
9
9
8
9
8
8
7
7
7
11
10
8
7
8
5
9
7
7
7
187
188
189
190
191
192
193
194
195
196
197
198
199
200
0
0
0
0
0
0
0
0
0
0
0
1
0
1
Finance
Finance
Marketing
No Major
Finance
Leadership
Marketing
Marketing
Marketing
Leadership
Marketing
No Major
Marketing
No Major
Unemployed
Unemployed
Unemployed
Full Time
Part Time
Unemployed
Unemployed
Full Time
Full Time
Unemployed
Unemployed
Unemployed
Unemployed
Unemployed
36
40
45
59
27
49
32
30
31
55
27
54
42
30
3.55
3.20
3.15
3.65
3.50
3.40
3.70
3.94
3.70
3.30
3.35
3.10
3.25
3.10
3.71
3.44
3.29
3.86
3.65
3.28
3.89
3.21
3.83
3.54
3.58
3.18
3.42
3.15
8
7
7
8
8
8
9
11
9
7
7
5
7
6
Works FT
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
Variable descriptions
Gender = 0 (female), 1 (male)
Major = student's major
Age = age of student in years
MBA_GPA = overall GPA in the MBA program
BS_GPA = overall GPA in the BS program
Hrs_Studying = average hours studied per week
Works FT = 0 (No), 1 (Yes)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
Unit 4
Practice Problems
Practice Problem One
Two Sample Hypothesis Test for the Mean (Independent Samples)
Level of Significance
0.05
Sample Mean
Sample Size
Sample Standard Deviation
No Pool
202763.158
38
33716.973
Standard Error (Computed)
Test Statistic (Computed)
8037.41
-2.80
Pool
225258.065
62
46371.959
This is a two-tailed test since we are testing if the mean is different for the houses with vs. without a pool.
The p-value of .0062 is less than .05, and so we reject the null hypothesis and conclude that the mean
sales price for homes is different for houses with vs. without a pool. The fact that the sample mean is
greater for houses with a pool indicates that houses with a pool likely have a higher mean price in the
population.
Two-Tailed Test
( )
Lower
Upper
Crit Value
Crit Value
-1.9600
1.9600
pValue
Decision
0.0062
Reject the null hypothesis
Home Prices with and without Pool
$230,000.00
$225,000.00
$220,000.00
$215,000.00
$210,000.00
$205,000.00
$200,000.00
$195,000.00
$190,000.00
No Pool
Pool
Unit 4
Practice Problems
Practice Problem Two
Two Sample Hypothesis Test for the Mean (Paired Samples)
Level of Significance
0.05
Standard Error (Computed)
Test Statistic (Computed)
3442.16
0.29
This is a two-tailed test since we are testing whether the mean appraisals given by the two agents are
different from one another. The p-value of 0.7720 is greater than .05, and so we fail to reject the null
hypothesis; there is insufficient evidence to conclude the mean appraisals are different for the two agents.
As a result we conclude that the two agents’ appraisals are not significantly different from one another.
Two-Tailed Test
Lower
Crit Value
Upper
Crit Value
p-Value
Decision
-1.9842
1.9842
0.7720
Do not reject the null
hypothesis
(d ) ( )
Comparison of Two Agents' Appraisals
$350,000
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
$0
1
11
21
31
41
Agent 1
51
61
Agent 2
71
81
91
Unit 4
Practice Problems
Practice Problem Three
Two Sample Hypothesis Test for the Proportion
Level of Significance
0.05
Number of Successes
Sample Size
Brick
30
40
Wood or Stucco
32
60
Proportion (Computed)
0.75
0.53
Z Test Statistic
(Computed)
2.19
This is an upper-tailed test since we are testing whether the proportion for brick homes with a pool is
greater than that of wood & stucco homes with a pool. The p-value of .0144 is less than .05, and so we
reject the null hypothesis. As a result, we conclude that brick homes are more likely to have a swimming
pool than wood & stucco homes.
Upper-Tail Test
H1: (P1 > P2 or P2 < P1)
Lower Crit
Value
Upper Crit
Value
pValue
Decision
n/a
1.6449
0.0144
Reject the null hypothesis
Relationship between Construction Type and Pools
100%
80%
Without Pool
60%
With Pool
40%
20%
0%
Brick
Wood or Stucco
Unit 4
Practice Problems
Practice Problem Four
Analysis of Variance
SUMMARY
Groups
2 BR
3 BR
4 BR
5 BR
Count
24
26
26
24
Sum
4807000.000
5574000.000
5552000.000
5738000.000
ANOVA
Source of Variation
Treatment
Error
SS
18885182948.718
166271407051.282
df
3
96
Total
185156590000.000
99
Average
200291.667
214384.615
213538.462
239083.333
MS
6295060982.906
1731993823.451
Variance
1904911231.884
1205046153.846
1457058461.538
2430688405.797
F
3.635
F crit
2.699
The p-value of .0156 is less than .05, and so we reject the null hypothesis. Thus we conclude that a
difference exists in the mean sales price based on number of bedrooms that a home has. Looking at the
Post Hoc tests, we see that homes with 5 bedrooms are worth significantly more than homes with 2, 3 or
4 bedrooms. There doesn't appear to be a significant difference in mean prices for homes with 2, 3 or 4
bedrooms.
Null hypothesis:
Alternate hypothesis:
Significance level:
p-Value
Decision:
= = =
Not all the means are equal
0.05
0.0156
Reject the null hypothesis
Mean Differences Post-Hoc Tests
Difference
Comparison
of Means
2 BR to 3 BR
2 BR to 4 BR
3 BR to 4 BR
2 BR to 5 BR
3 BR to 5 BR
4 BR to 5 BR
14092.949
13246.795
846.154
38791.667
24698.718
25544.872
Lower
Conf. Limit
-9291.274
-10137.428
-22065.612
14944.345
1314.495
2160.649
Upper
Conf. Limit
37477.172
36631.018
23757.920
62638.989
48082.941
48929.095
Difference in
Treatment
Means???
- no difference - no difference - no difference ***Means are different***
***Means are different***
***Means are different***
Unit 4
Practice Problems
Practice Problem Four (continued)
Comparison of Number of Bedrooms and
Home Price
$240,000
$230,000
$220,000
$210,000
$200,000
$190,000
$180,000
2 BR
3 BR
4 BR
5 BR
Two Sample Hypothesis Test for the Mean (Independent Samples)
Level of Significance
0.05
Sample Mean
Sample Size
Sample Standard Deviation
Group 1
100
30
10
Standard Error (Computed)
Test Statistic (Computed)
1.99
-2.51
Group 2
105
40
5
Lower Crit Value
Upper Crit Value
p -Value
Two-Tailed Test
H1: (m1 m2)
-1.9600
1.9600
0.0143
Upper-Tail Test
H1: (m1 > m2 OR m2 < m1)
n/a
1.6449
0.9929
Lower-Tail Test
H1: (m1 < m2 OR m2 > m1)
-1.6449
n/a
0.0071
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
dent Samples)
Decision
Reject the null hypothesis
Do not reject the null hypothesis
Reject the null hypothesis
at H1 is true.
ence to conclude that H1 is true.
NNOT ACCEPT the null).
Two Sample Hypothesis Test for the Mean (Independent Samples)
Group 1
Group 2
2
4
9
3
2
3
7
5
8
4
3
Level of Significance
0.05
Sample Mean
Sample Size
Sample Standard Deviation
Group 1
4.000
5
2.915
Standard Error (Computed)
Test Statistic (Computed)
1.51
-0.66
Group 2
5.000
6
2.098
Lower
Crit Value
Upper
Crit Value
p -Value
Two-Tailed Test
H1: (m1 m2)
-2.2622
2.2622
0.5245
Upper-Tail Test
H1: (m1 > m2 OR m2 < m1)
n/a
1.8331
0.7392
Lower-Tail Test
H1: (m1 < m2 OR m2 > m1)
-1.8331
n/a
0.2608
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude th
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the
©2007 DrJimMirabella.com
nt Samples)
Decision
Do not reject the null hypothesis
Do not reject the null hypothesis
Do not reject the null hypothesis
conclude that H1 is true.
ufficient evidence to conclude that H1 is true.
e (i.e., we CANNOT ACCEPT the null).
Two Sample Hypothesis Test for the Mean (Paired Samples)
Item
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Condition 1
Condition 2
135
110
131
142
105
130
131
110
125
149
128
105
119
140
98
123
127
115
122
145
Level of Significance
0.05
Standard Error (Computed)
Test Statistic (Computed)
4.40
3.30
Lower
Crit Value
Two-Tailed Test
H1: (md 0), (m1 m2)
-2.2622
Upper-Tail Test
H1: (md > 0), (m1 > m2 OR m2 < m1)
n/a
Lower-Tail Test
H1: (md < 0), (m1 < m2 OR m2 > m1)
-1.8331
If you REJECT the null hypothesis, conclu
If you DO NOT REJECT the null hypothesis, there is insufficie
NEVER conclude that the null hypothesis is true (i.e.,
©2007 DrJimMirabella.com
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
Upper
Crit Value
p -Value
Decision
2.2622
0.0092
Reject the null hypothesis
1.8331
0.0046
Reject the null hypothesis
n/a
0.9954
Do not reject the null hypothesis
T the null hypothesis, conclude that H1 is true.
pothesis, there is insufficient evidence to conclude that H1 is true.
null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
Two Sample Hypothesis Test for the Proportion
Level of Significance
0.05
Number of Successes
Sample Size
Group 1
60
100
Group 2
140
200
Proportion (Computed)
0.60
0.70
Z Test Statistic (Computed)
-1.73
Lower Crit Value
Upper Crit Value
p -Value
Two-Tailed Test
H1: (P1 P2)
-1.9600
1.9600
0.0833
Upper-Tail Test
H1: (P1 > P2 or P2 < P1)
n/a
1.6449
0.9584
Lower-Tail Test
H1: (P1 < P2 or P2 > P1)
-1.6449
n/a
0.0416
If you REJECT the null hypothesis, conclude that H1 is true.
If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.
NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).
©2007 DrJimMirabella.com
Decision
Do not reject the null hypothesis
Do not reject the null hypothesis
Reject the null hypothesis
at H1 is true.
ence to conclude that H1 is true.
NNOT ACCEPT the null).
ANOVA
Analysis of Variance
Group A
18,5
24
17,2
19,9
18
17,99
17,48
16,97
16,46
15,95
15,44
14,93
14,42
13,91
13,4
12,89
12,38
11,87
11,36
10,85
10,34
9,83
17,2
19,9
18
Group B
26,3
25,3
24
21,2
24,5
21,95
21,18
20,41
19,64
18,87
18,1
17,33
16,56
15,79
15,02
14,25
13,48
12,71
11,94
11,17
Group C
20,6
25,2
20,8
24,7
22,9
24,07
24,48
24,89
25,3
25,71
26,12
26,53
26,94
27,35
27,76
Group D
25,4
19,9
22,6
17,5
20,4
17,44
16,2
14,96
13,72
12,48
Group E
12,48
14,96
17,44
17,5
19,9
SUMMARY
Groups
Group A
Group B
Group C
Group D
Group E
ANOVA
Source of Variation
Treatment
Error
Total
Null hypothesis:
Alternate hypothesis:
Significance level:
p-Value
Decision:
Count
25
20
15
10
5
Sum
389,170
369,700
373,350
180,600
82,280
Average
15,567
18,485
24,890
18,060
16,456
Variance
11,968
21,215
4,543
16,343
7,991
SS
849,633
932,971
df
4
70
MS
212,408
13,328
F
15,937
1782,604
74
287,2369
403,0815
63,599
147,088
31,96592
3,650776
F crit
2,503
m1 = m2 = m3 = m4 = m5
Not all the means are equal
0,05
0,0000
Reject the null hypothesis
Mean Differences Post-Hoc Tests
Difference
Comparison
of Means
Group A to Group B
2,918
Group A to Group C
9,323
Group B to Group C
6,405
Group A to Group D
2,493
Group B to Group D
0,425
Group C to Group D
6,830
Group A to Group E
0,889
Group B to Group E
2,029
Group C to Group E
8,434
Group D to Group E
1,604
Lower
Conf. Limit
0,734
6,945
3,918
-0,231
-2,395
3,857
-2,678
-1,612
4,674
-2,384
Upper
Conf. Limit
5,103
11,701
8,892
5,218
3,245
9,803
4,456
5,670
12,194
5,592
©2007 DrJimMirabella.com
Difference in
Treatment Means???
***Means are different***
***Means are different***
***Means are different***
- no difference - no difference ***Means are different***
- no difference - no difference ***Means are different***
- no difference -
Group A
Group B
Group C
Group D
Group E
17,023
20,113
26,770
20,363
17,626
14,111
16,857
23,010
15,757
15,286
15,567
18,485
24,890
18,060
16,456
Confidence Intervals of Groups
30
26,770
25
23,010
20,363
20,113
20
17,023
17,626
16,857
15,757
15
15,286
14,111
10
5
0
Group A
Group B
Group C
Group D
Group E
Sample Size Determination for Proportion
Estimate of True Proportion* =
Sampling Error =
Confidence Level =
Finite Population Size =
0.50
0.05
95.00%
Sample Size Needed =
385
500
Sample Size Needed =
218
*Use .50 for the "estimate of true proportion" when unknown.
Sample Size Determination for Mean
Population Standard Deviation =
Sampling Error =
Confidence Level =
Finite Population Size =
100
25
95.00%
Sample Size Needed =
62
500
Sample Size Needed =
55
©2007 DrJimMirabella.com
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