Solutions of QUIZ 6. M262 Section 1. (27.04.2022).
1. A study is to be made of the relative effectiveness of two kinds of cough medicines
in increasing sleep. Seven people with colds are given medicine A the first night and
medicine B the second night. Their hours of sleep each night are recorded.
The hours of sleep of 7 people in the first night are 4.9, 4.2, 5.9, 5.0, 5.2, 7,5, 6.3,
respectively.
The hours of sleep of 7 people in the second night are 4.0, 4.3, 5.1, 5.0, 5.3, 7,2, 6.0,
respectively.
At α = 0.1 test to determine if there is a significant difference in the effectiveness of two
kinds of cough medicines in increasing sleep.
Solution:
H0 : µ1 = µ2
H1 : µ1 6= µ2
For α = 0.1 and d = 7 − 1 = 6 we have tα/2 = 1.943. Therefore, the rejection region is
(−∞, −1.943, 1.943, ∞).
0.9 − 0.1 + 0.8 + 0 − 0.1 + 0.3 + 0.3
D̄ = = 0.3
7
2 (0.9 − 0.3)2 + (−0.1 − 0.3)2 + · · · + (0.3 − 0.3)2 + (0.3 − 0.3)2
SD = = 0.17
7−1
D̄
Therefore, √ = 1.925. Since 1.925 is not in the rejection region, we do not reject
SD / n
H0 and do not accept H1 : there is no sufficient evidence in the difference between two
kinds of cough medicines in increasing sleep.
1
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:13:09 GMT -05:00
https://www.coursehero.com/file/249824288/22262q6solpdf/
1. A study is to be made of the relative effectiveness of two kinds of cough medicines
in increasing sleep. Seven people with colds are given medicine A the first night and
medicine B the second night. Their hours of sleep each night are recorded.
The hours of sleep of 7 people in the first night are 4.9, 4.2, 5.9, 5.0, 5.2, 7,5, 6.3,
respectively.
The hours of sleep of 7 people in the second night are 4.0, 4.3, 5.1, 5.0, 5.3, 7,2, 6.0,
respectively.
At α = 0.1 test to determine if there is a significant difference in the effectiveness of two
kinds of cough medicines in increasing sleep.
Solution:
H0 : µ1 = µ2
H1 : µ1 6= µ2
For α = 0.1 and d = 7 − 1 = 6 we have tα/2 = 1.943. Therefore, the rejection region is
(−∞, −1.943, 1.943, ∞).
0.9 − 0.1 + 0.8 + 0 − 0.1 + 0.3 + 0.3
D̄ = = 0.3
7
2 (0.9 − 0.3)2 + (−0.1 − 0.3)2 + · · · + (0.3 − 0.3)2 + (0.3 − 0.3)2
SD = = 0.17
7−1
D̄
Therefore, √ = 1.925. Since 1.925 is not in the rejection region, we do not reject
SD / n
H0 and do not accept H1 : there is no sufficient evidence in the difference between two
kinds of cough medicines in increasing sleep.
1
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:13:09 GMT -05:00
https://www.coursehero.com/file/249824288/22262q6solpdf/
