Answers to HW – 2 sample means
m  mean summer earnings for male students
1.  F  mean summer earnings for female students
m   F  difference in mean summer earnings between male and female students
 H o : m   F  0

 H A : m   F  0
t
7.81
t
x
m

 x F   m   F 
sm2 sF2

nm nF
1884.52  1360.39   0  7.81
1368.37 2 1037.46 2

675
621
P  Value  P (t  7.81)  tcdf (7.81, , 620)  0
df  620
Aspt: 1. Independent Random samples
2. Approximately normal since
nm  30

nF  30
Reject Ho since p-value (0) <α.(.05)
There’s sufficient evidence to support the claim that the
mean summer earning of male students is greater than
that of female students.
Use T-Test since σm and σF
are unknown
 A  mean number of runs scored in the American League
2.  N  mean number of runs scored in the National League
 A   N  difference in mean number of runs cored in American & National Leagues
Ho :  A  N  0

H A :  A  N  0
t
0.509
t
Aspt: 1. Independent Random samples
2. Approx. normal (Boxplots somewhat symmetrical)
n  30
Since  A
nN  30
Use a 2-Sample T-Test
x
m

 x F   m   F 
sm2 sF2

nm nF
 9.807  9.581  0  0.509
0.8052 1.5492

14
16
P  Value  P (t  .509)  tcdf (.509, ,13)  0.308
df  13
Fail to Reject Ho since p-value >α.
There’s insufficient evidence to support the claim that
the mean number of runs scored in the American League
is greater than the mean number of runs cored in the
National League.
3.
1  mean score from morning class
2  mean score from afternoon class
1  2  difference in mean scores
t
t
 H o : 1  2  0

 H A : 1  2  0
x
m

 x F   m   F 
sm2 sF2

nm nF
 900  920   0  2.18
502 302

40 42
P  Value  P (t  2.18)  tcdt (, 2.18,39)  0.0177
0.509
Aspt: 1. Independent Random samples
2 Approximately normal since
n1  30

n2  30
Use a 2-Sample T-Test
df  39
Reject Ho since p-value <α.
There’s sufficient evidence to support the claim that the
mean score of the morning class is lower than the mean
score of the afternoon class.
1  mean skull size from 4000 B.C.E.
4. 2  mean skull size from 2000 B.C.E.
1  2  difference in mean skull size from 4000 B.C.E. to 2000 B.C.E.
t
 H o : 1  2  0

 H A : 1  2  0
t
x
m

 x F   m   F 
sm2 sF2

nm nF
131.1  135.6   0  3.90
4.922 4.042

30
30
P  Value  tcdf (, 3.9, 29) * 2  0
df  29
Aspt: 1. Independent Random samples
2. Approximately normal since
n1  30

n2  30
Use a 2-Sample T-Test
Reject Ho since p-value <α.
There’s sufficient evidence to support the claim that the
mean skull size from 4000 B.C.E. is different from the
mean skull size from 2000 B.C.E.
1  mean time to extinguish the fire with type I extinguisher
5. 2  mean time to extinguish the fire with type II extinguisher
1  2  difference in mean time to extinguish the fire with type I ex. & type II.
t
 H o : 1  2  0

 H A : 1  2  0
t
x
m

 x F   m   F 
sm2 sF2

nm nF
12.2  15   0  1.73
2.82 2.82

6
6
P  Value  tcdf (, 1.73,5)  0.057
df  5
Aspt: 1. Independent Random samples
3 Approximately normal since
(Boxplot somewhat symm)
n1  30

n2  30
Use a 2-Sample T-Test
Fail to Reject Ho since p-value >α.
There’s insufficient evidence to support the claim that
the mean time to extinguish the fire with type I is less
than the mean time to extinguish with type II.
6.   mean tip amount
x
s
n
5.25  4.75
t
 2.04
1.15
22
P  Value  0.027
t
 H o :   4.75

 H A :   4.75
df  21
Aspt: 1. Simple Random samples
2. Not Approximately normal since
n  30
Use a 1-Sample t-Test
Fail Reject Ho since p-value >α.
There’s insufficient evidence to support the claim that
the mean tip is more than $4.75