Question

(1 point) Ten randomly selected people took an IQ test A, and the next day they took a very similar IQ test B. Their scores are shown in the table below.

Person | A | B | C | D | E | F | G | H | I | J |

Test A | 102 | 107 | 88 | 109 | 77 | 96 | 99 | 117 | 83 | 128 |

Test B | 101 | 108 | 91 | 112 | 78 | 100 | 102 | 119 | 84 | 130 |

1. Consider (Test A - Test B). Use a 0.05 significance level to
test the claim that people do better on the second test than they
do on the first.

(a) What test method should be used?

**A.** Two Sample z

**B.** Two Sample t

**C.** Matched Pairs

(b) The test statistic is

(c) The critical value is

(d) Is there sufficient evidence to support the claim that
people do better on the second test?

**A.** No

**B.** Yes

2. Construct a 95% confidence interval for the mean of the
differences. Again, use (Test A - Test B).

<?<<μ<

Answer #1

Step 1

**C.** Matched Pairs

To Test :-

H0 :- µd = 0

H1 :- µd < 0

Test Statistic :-

S(d) = √(Σ (di - d̅)2 / n-1)

S(d) = √(18.9 / 10-1) = 1.4491

d̅ = Σ di/n = -19 / 10 = -1.9

t = d̅ / ( S(d) / √(n) )

t = -1.9 / ( 1.4491 / √(10) )

t = -4.1461

Test Criteria :-

Reject null hypothesis if t < - t(α)

Critical value t(α) = t(0.05) = 1.83311

t < - t(α) = -4.1461 < -1.83311

**Result :- Reject null hypothesis**

**B.** Yes, we support the claim that
people do better on the second test.

Step 2

Confidence Interval :-

d̅ ± t(α/2, n-1) Sd / √(n)

t(α/2) = t(0.05 /2) = 1.8331

-1.9 ± t(0.05/2) * 1.4491/√(10)

Lower Limit = -1.9 - t(0.05/2) 1.4491/√(10)

Lower Limit = -2.9365

Upper Limit = -1.9 + t(0.05/2}) 1.4491/√(10)

Upper Limit = -0.8635

**95% Confidence interval is ( - 2.9365 , - 0.8635
)**

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
108
114
127
110
101
77
99
96
82
89
Test B
109
115
127
115
105
75
101
100
85
91
Consider (Test A - Test B). Use a 0.01 significance level to test
the claim that people...

Please show all steps
Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
77
113
97
107
95
128
100
88
112
84
Test B
76
116
101
108
96
127
99
87
112
85
1. Consider (Test A - Test B). Use a 0.010.01 significance level to...

Ten randomly selected
people took IQ test A, and next day they took a very similar IQ
test B. Their scores are shown in the table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
101
112
99
73
91
113
93
105
124
82
Test B
102
117
98
74
92
110
92
108
125
83
Calculate (Test B - Test A) to find the differences. Use a = .05
significance level to test...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
104
87
88
110
97
128
116
94
71
101
Test B
110
88
89
108
96
129
119
97
73
106
1. Consider (Test A - Test B). Use a 0.050.05 significance level to
test the claim that...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below. Person A B C D E F G H I J Test A 100 96 89 101 72 121
105 85 111 113 Test B 101 100 89 105 73 122 108 88 109 120 1.
Consider (Test A - Test B). Use a 0.01 0.01 significance level to
test the claim...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below. Person A B C D E F G H I J Test A 84 102 105 122 79 96
94 110 89 113 Test B 84 104 107 125 82 99 94 112 92 113 1. Consider
(Test A - Test B). Use a 0.05 significance level to test the claim
that...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
106
87
89
102
108
126
113
94
98
78
Test B
111
88
92
101
111
128
112
92
99
79
1. Consider (Test A - Test B). Use a 0.05 significance level to
test the claim that...

(6 pts) Ten randomly selected people took an IQ test A, and next
day they took a very similar IQ test B. Their scores are shown in
the table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
104
90
109
73
118
81
93
130
108
100
Test B
104
90
109
75
119
81
92
129
108
104
1. Consider (Test A - Test B). Use a 0.05 significance level to
test the...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below. Person A B C D E F G H I J Test A 93 104 79 90 98 81
111 113 107 121 Test B 92 105 80 88 101 81 110 109 113 124 1.
Consider (Test A - Test B). Use a 0.01 0.01 significance level to
test the claim...

Ten randomly selected people took an IQ test A, and next day
they took a very similar IQ test B. Their scores are shown in the
table below.
Person
A
B
C
D
E
F
G
H
I
J
Test A
115
105
80
90
125
81
104
99
108
94
Test B
115
103
80
91
124
81
107
99
106
92
1. Consider (Test A - Test B). Use a 0.01 significance level to
test the claim that...

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