ch9 - hypothesis test
1.
Statistics
Given n = 60, X = 22,  = 30, at the confident level 0.05 test the
2.
following hypothesis.
Ans.
H0 :
H1:
  20,
 > 20,
Repeat the above question with n = 60, X = 22,  = 10
Step (3) and (4) are same as above.
Step (5): Collect data, compute Z, make decision and interpret
the result.
Ans.
Step (3): Since sample size is large enough and  is known, we
will use the following z statistics:
22  20
Z=
X  0
Z=
So, we accept H0. The data does not show that the population
mean is greater than 20.
/ n
Step (4): Reject H0 if computed Z > 1.645.
3.
Otherwise Accept H0
Ans.
Step (5): Collect data, compute Z, make decision and interpret
the result.
22  20
Z=
10 / 60 = 1.549193
Repeat the above question with n = 30, X = 22,  = 10
Step (3) and (4) are same as above.
Step (5): Collect data, compute Z, make decision and interpret
the result.
22  20
30 / 60 = 0.516398
Z=
So, we accept H0. The data doesn’t show that the population
mean greater than 20.
10 / 30 = 1.095445
So, we accept H0. The data does not show that the population
mean is greater than 20
1/3
ch9 - hypothesis test
4.
Statistics
Given n = 60, X = 22, s = 10, at the confident level 0.05 test the
5.
following hypothesis.
assumption that the underlying distribution is normal.
= 20,
  20,
H0 :
H1:
Ans.
Repeat the above question with n = 20, X = 22, s = 10 and the
Step (3): Since sample size is large enough, we will use the
following t statistics:
Ans.
Step (3): Since underlying distribution is normal, we will use
the following t statistics:
X  0
t=
= 20,
  20,
H0 :
H1:
X  0
t=
s/ n
s/ n
(df = 20 – 1 = 19)
Step (4): Reject H0 if computed t > 1.96 or <-1.96
Step (4): Reject H0 if computed t > 2.093 or <-2.093
Otherwise Accept H0
Otherwise Accept H0
Step (5): Collect data, compute t, make decision and interpret
Step (5): Collect data, compute t, make decision and interpret
the result.
the result.
22  20
22  20
t=
t=
10 / 60 = 1.549193
10 / 20 = 1.549193
So, we accept H0. The data doesn’t show that the population
mean different from 20.
So, we accept H0. The data doesn’t show that the population
mean different from 20.
2/3
ch9 - hypothesis test
6.
Statistics
I flipped a coin 100 times. Among that 100 times, I got 58 head.
At the confident level 0.01 test the following hypothesis.
7. Repeat the above question with P = 0.60 and n = 100.
Ans. Step (3) and (4) are the same.
Step (5): Collect data, compute Z, make decision and interpret
the result.
H0:
 = 0.5
H1:
  0.5
where  = the probability that you will get a head.
0.60  0.5
Z=
Ans. Step (3): Since sample size is large enough (both n and n(1-)
greater than 5), we will use the following z statistics:
P  0
Z=
0 (1  0 ) , 0 = 0.5
n
Step (4): Reject H0 if computed Z >2.576 or < -2.576
Otherwise accept H0.
Step (5): Collect data, compute Z, make decision and interpret
the result.
0.58  0.5
Z=
0.5(1- 0.5) = 1.6
100
So, we accept H0. The data does not show the coin is unfair.
3/3
0.5(1- 0.5) = 2
100
So, we accept H0. The data does not show the coin is unfair.