A B C D E F G H I J K L
1 Hypothesis Testing - Population Mean
2
3 Evidence
4 Sample size 80 n
5 Sample Mean 163.2601 x-bar
6
7 s Known; Normal Population or Sample Size >= 30 Correction for Finite Population
8 Population Stdev. 76.59452621 s Population size N
9 Test Statistic -0.6353 z Test Statistic z
10 At an a of At an a of
11 Null Hypothesis p-value 5% p-value 5%
12 H0: m = 168.7007574 0.5252
13 H0: m ³ 168.7007574 0.2626
14 H0: m £ 168.7007574 0.7374
15
16
17 Evidence
18 Sample size 35 n
19 Sample Mean 152 x-bar
20 Sample Stdev. 1.6 s
21
22 s Unknown; Population Normal
23 Test Statistic -3.6975 t
24 At an a of
25 Null Hypothesis p-value 5%
26 H0: m = 153 0.0008 Reject
27 H0: m ³ 153 0.0004 Reject
28 H0: m £ 153 0.9996
29
A B CD E F G H I J K L M N
1 Hypothesis Testing - Population Mean Example 7-6
2
3 Sample Evidence
4 Data Sample size 37 n
5 1 1998.41 Sample Mean 1999.54 x-bar
6 2 2000.34
7 3 2001.68 s Known; Normal Population or Sample Size >= 30 Correction for Finite Population
8 4 2000.98 Population Stdev. 1.8 s Population size N
9 5 2000.89 Test Statistic -1.5472 z Test Statistic z
10 6 2001.07 At an a of At an a of
11 7 1997.01 Null Hypothesis p-value 5% p-value 5%
12 8 2000.34 H0: m = 2000 0.1218
13 9 1997.86 H0: m ³ 2000 0.0609
14 10 1998.43 H0: m £ 2000 0.9391
15 11 1998.12
16 12 1997.85
17 13 2000.25 Evidence
18 14 1997.65 Sample size 37 n
19 15 2001.17 Sample Mean 1999.54 x-bar
20 16 1997.44 Sample Stdev. 1.36884 s
21 17 1998.7
22 18 1998.67 s Unknown; Population Normal
23 19 1997.58 Test Statistic -2.0345 t
24 20 2000.28 At an a of
25 21 1998.89 Null Hypothesis p-value 5%
26 22 2000.13 H0: m = 2000 0.0493 Reject
27 23 2000.1 H0: m ³ 2000 0.0247 Reject
28 24 2000.39 H0: m £ 2000 0.9753
29 25 2001.27
30 26 1998.98
31 27 2000.21
32 28 2000.36
33 29 2000.17
34 30 1998.67
35 31 2001.68
36 32 2000.76
37 33 1998.53
38 34 1998.24
39 35 1998.18
40 36 2000.67
41 37 2001.11
42
A B C D E F G H I J K L M
1 Sample Size Determination for Testing m
2
3 Assumption
4 H0: m >= 1000 Either Normal Population Tabulation of required sample size
5 Popn. Stdev. 10 s Or n >= 30 ###
6 Significance Level 5.00% a Actual m
7 : 994 995 996 997
8 Probability of Type II Error 5.0% 31 44 68 121
9 When m = 995 6.0% 29 41 64 114
10 Desired Maximum 8.00% b 7.0% 28 39 61 109
b
11 8.0% 26 38 59 104
12 Required Sample Size 38 n 9.0% 25 36 56 100
13 10.0% 24 35 54 96
14
15
16 Plot of Required Sample Size
17
18
19
20 150
21 100
22
23
50
24 0 Sample Size
25 5.0%
26 6.0%
27
997
7.0%
28
Beta
8.0%
996
29
30 9.0%
Actual Popn. Mean
995
31 10.0%
32
994
33
A B C D E F G H I J K L M N O P Q R S T
1 Type I and Type II Error probabilities
2 Tabulation of b when m = 994
3
4 Data Assumption a
5 H0: m >= 1000 Either Normal Population 0.5% 0.3% 0.4% 0.5% 0.6% 0.8% 1.0% 1.2% 2.0% 4.0% 10.0%
6 Popn. Stdev. 10 s Or n >= 30 30 30% 26% 24% 22% 19% 17% 15% 11% 6% 2%
7 1-Tail test 35 21% 18% 17% 15% 13% 11% 10% 7% 4% 1%
8
n 40 15% 13% 11% 10% 8% 7% 6% 4% 2% 1%
9 50 7% 6% 5% 4% 3% 3% 2% 1% 1% 0%
10
11
35%
12
13
18 30%
19
20 25%
21
30
22 20%
b
35
23
40
24
15% 50
25
26
27 10%
28
29 5%
30
31 0%
32 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0%
33 a
34
35
A B C D E F G H I J
1 Power Curve for a m Test
2 Assumption:
3 Either Normal Population
4 Or n >= 30
5
6 H0: m >= 1000 When m = 996
7 Popn. Stdev. 10 s P(Type II Error) 0.1881
8 Sample Size 40 n Power 0.8119
9 Significance Level 5% a
10
11
1.00
12
13 0.90
14
0.80
15
Power
16 0.70
17
0.60
18
19 0.50
20
0.40
21
22 0.30
23
0.20
24
25 0.10
26
27 0.00
992 993 994 995 Actual m
996 997 998 999 1000 1001
28
29
A B C D E F G H I J K
1 Operating Characteristic Curve
2 Assumption: 2-T left limit
3 Either Normal Population Tabulation
4 Or n >= 30 m
5 ###
6 H0: m >= 1000 ###
7 Popn. Stdev. 10 s Sample Size 40 n1 ###
8 Significance Level 10% a Sample Size 100 n2 ###
9 ###
10 ###
11 1.00 ###
12 ###
P(Accept H0)
0.90
13 ###
14 0.80
###
15 ###
16 0.70 ###
17 Legend
0.60
18 n = 40
19 0.50 n = 100
20 ###
21 0.40 ###
22 ###
0.30
23 ###
24 0.20 ###
25 ###
0.10
26 ###
27 0.00 ###
28 990 992 994 Actual
996 m998 1000 1002 1004 ###
29 ###
