final review answers. two-tailed t test solution -1 h 0 : h a : = df = critical value(s): test...
TRANSCRIPT
Final Review Answers
Two-Tailed t Test Solution -1
• H0: • Ha: • = • df = • Critical Value(s):
Test Statistic:
Decision:
= 368 368
.05
25 - 1 = 24
t0 2.064-2.064
.025
Reject H0 Reject H0
.025
372.5 3684.5
5
25
Xt
S
n
Reject at = .05
P-value = 0
Two-Tailed Z Test Solution -2
• H0: • Ha: • = • n = • Critical Value(s):
Test Statistic:
Decision:
= 70
70
.05
36
Z0 1.96-1.96
.025
Reject H 0 Reject H0
.025
69.7 70.51
3.5
36
XZ
n
Do not reject at = .05
One-Tailed Z Test Solution -3
• H0: • Ha: • = • n =• Critical Value(s):
Test Statistic:
Decision:
= 32 < 32
.01
60
Z0-2.33
.01
Reject
30.7 322.65
3.8
60
XZ
n
Reject at = .01
Two-Tailed t Test Solution-4
• H0: • Ha: • • df • Critical Value(s):
Test Statistic:
Decision:
= 3.25
3.25
.01
64 - 1 = 63
t0 2.656-2.656
.005
Reject H0 Reject H0
.005
3.238 3.25.82
.117
64
Xt
S
n
Do not reject at = .01
One-Tailed t Test Solution - 5
• H0: • Ha: • =• df =• Critical Value(s):
Test Statistic:
Decision:
= 140
< 140
.0520 - 1 = 19
t0-1.729
.05
Reject H0
138.47 1402.57
2.66
20
Xt
S
n
Reject at = .05
One-Tailed t Test Solution -6
• H0: • Ha: • = • df = • Critical Value(s):
Test Statistic:
Decision:
= 5 < 5
.05
10 - 1 = 9
t0 1.833
.05
Reject H0
6.4 51.31
3.373
10
Xt
S
n
Do not reject at = .05
One-Proportion Z Test Solution - 7
• H0: • Ha: • = • n =• Critical Value(s):
Test Statistic:
Decision:
p = .10
p < .10
.05
200
Z0-1.645
.05
Reject H0
0
0 0
11.10ˆ 200 2.12
.10 .90200
p pZ
p qn
Reject at = .05
One-Proportion Z Test Solution - 8
• H0: • Ha: • = • n = • Critical Value(s):
Test Statistic:
Decision:
p = .04
p .04
.05
500
Z0 1.96-1.96
.025
Reject H 0 Reject H0
.025
0
0 0
25.04ˆ 500 1.14
.04 .96500
p pZ
p qn
Do not reject at = .05
1. Miles per gallon ratings of cars before and after mounting radial tires - DEPENDENT
2. The life expectancy of light bulbs made in two different factories - INDEPENDENT
3. Difference in hardness between two metals: one contains an alloy, one doesn’t - INDEPENDENT
4. Tread life of two different motorcycle tires: one on the front, the other on the back - DEPENDENT
9
• H0:• Ha:• • df • Critical Value(s):
1 - 2 = 0 (1 = 2)
1 - 2 0 (1 2)
.05
11 -1 = 10
t0 2.228-2.228
.025
Reject H 0 Reject H0
.025
Small-Sample Test Solution 10-A
1 2 1 2
2 22 21 2
1 2
3.27 2.53 01.43
1.30 1.1611 15
X Xt
S Sn n
Test Statistic:
Do not reject at = .05
• H0:• Ha:• • df • Critical Value(s):
1 - 2 = 1% (1 = 2)
1 - 2 < 1% (1 2)
.05
11 -1= 10
Small-Sample Test Solution 10-B
1 2 1 2
2 22 21 2
1 2
3.27 2.53 10.505
1.30 1.1611 15
X Xt
S Sn n
Test Statistic:
Do not reject at = .05
t0-1.812
.05
Reject H0
Large-Sample Test Solution - 11
• H0:• Ha:• • n1 = , n2 =• Critical Value(s):
t0 1.761-1.761
.05
Reject H0 Reject H0
.05
1 - 2 = 0 (1 = 2)
1 - 2 0 (1 2).10
15 15 1 2 1 2
2 22 21 2
1 2
6012 5832 00.86
602 49715 15
X Xt
S Sn n
Do not reject at = .10
Paired-Difference Solution-12
• H0:• Ha: • = • df =• Critical Value(s):
d = 0 (d = A - B)
d < 0
.10
4 - 1 = 3
t0-1.638
.10
Reject H0
Computation Table
Observation Before After Difference
Sam 85 94 9
Tamika 94 87 -7
Brian 78 79 1
Mike 87 88 1
Total 4
d = 1 Sd = 6.53
Test Statistic:
Decision:
Do not reject at = .10
0 1 0.306
6.53
4d
d
d Dt
S
n
• H0: • Ha: • = • n1 = n2 = • Critical Value(s):
p1 - p2 = 0
p1 - p2 0
.0178 82
z0 2.58-2.58
Reject H0 Reject H0
.005 .005
Test for Two Proportions Solution -13
1 21 2
1 2
63 49ˆ ˆ.808 .598
78 82
X Xp p
n n
.808 .598 0
(.808)(.192) (.598)(.402)78 82
2.90
Z
Reject at = .01
• H0:• Ha:• = • nMA = nCA =• Critical Value(s):
pMA – pCA = 0
pMA – pCA < 0
.05
1500 1500
Z0-1.645
.05
Reject H0
Test for Two Proportions Solution - 14
74 129ˆ ˆ.0493 .0860
1500 1500
CAMAMA CA
MA CA
XXp p
n n
.0493 .0860 0
(.0493)(.9507) (.0860)(.914)1500 1500
4.01
Z
Reject at = .05
• H0:• Ha:• =• n1 = n2 = n3 =• Critical Value(s):
p1 = p2 = p3 = 1/3
At least 1 is different
.05
63 45 72
= .05
c20
Reject H0
5.991
2 Test for k Proportions Solution - 15
,0
1 2 3 180 1 3 60
i iE n np
E n E n E n
2
2
all cells
2 2 263 60 45 60 72 60
6.360 60 60
i i
i
n E n
E n
Reject at = .05
2 Test of Independence Solution - 16
• H0: • Ha: • = • df = • Critical Value(s):
No Relationship
Relationship
.05
(2 - 1)(2 - 1) = 1
c20
Reject H0
3.841
= .05
House Location Urban Rural
House Style Obs. Exp. Obs. Exp. Total
Split-Level 63 54.6 49 57.4 112
Ranch 15 23.4 33 24.6 48
Total 78 78 82 82 160
112·82 160
48·78 160
48·82 160
112·78 160
2
2
all cells
2 2 2
11 11 12 12 22 22
11 12 22
2 2 263 54.6 49 57.4 33 24.6
8.4154.6 57.4 24.6
ij ij
ij
n E
E
n E n E n E
E E E
Reject at = .05
2 Test of Independence Solution -17
• H0: • Ha: • = • df = • Critical Value(s):
No Relationship
Relationship
.05
(2 - 1)(2 - 1) = 1
c20
Reject H0
3.841
= .05
Diet Pepsi No Yes
Diet Coke Obs. Exp. Obs. Exp. Total
No 84 53.5 32 62.5 116
Yes 48 78.5 122 91.5 170
Total 132 132 154 154 286
170·132 286
170·154 286
116·132 286
154·132 286
2
2
all cells
2 2 2
11 11 12 12 22 22
11 12 22
2 2 284 53.5 32 62.5 122 91.5
54.2953.5 62.5 91.5
ij ij
ij
n E
E
n E n E n E
E E E
Reject at = .05