Question
In: Statistics and Probability
Assume that both populations are normally distributed. a) Test whether 2μ1≠μ2 at the α=0.05 level of...
|
Assume that both populations are normally distributed. a) Test whether 2μ1≠μ2 at the α=0.05 level of significance for the given sample data. b) Construct a 95% confidence interval about 2μ1−μ2. |
Sample 1 |
Sample 2 |
|||
|---|---|---|---|---|---|
|
n |
19 |
19 |
|||
|
x overbarx |
11.7 |
14.4 |
|||
|
s |
3.4 |
3.9 |
|||
Solutions
Expert Solution
SOLUTION:
From given data,
Assume that both populations are normally distributed
| Sample 1 | Sample 2 | |
 |
 = 19 |
 = 19 |
 |
=11.7 |
 =
14.4 |
 |
 = 3.4 |
 = 3.9 |
a) Test whether 2μ1≠μ2 at the α=0.05 level of significance for the given sample data
H0 : 2μ1 = μ2 ( Null hypothesis )
H1 : 2μ1 ≠ μ2 ( Alternative hypothesis )
-
=
11.7 - 14.4 = -2.7
SE( -
) =
= 
= 1.18699
Test statistic : t = ( -
) /
SE( -
)
= -2.7 / 1.18699
= - 2.2746
t = - 2.2746
degree of freedom =df = + - 2
= 19 + 19 -2 = 36
α=0.05 = > critical value = tcritical = 
2.028
b) Construct a 95% confidence interval about 2μ1−μ2
95% confidence interval is
( -
)
tcritical * SE( -
)
- 2.7 2.028 * 1.18699
- 2.7 2.407215
( - 2.7 - 2.407215 ) , ( - 2.7+ 2.407215 )
-5.1072 , -0.2927
confidence interval about 2μ1−μ2 is from -5.10 to -0.29
orchestra answered 2 years agoRelated Solutions
1, Assume that both populations are normally distributed. (a) Test whether μ1≠μ2 at the α=0.05 level...
1, Assume that both populations are normally distributed.
(a) Test whether μ1≠μ2 at the α=0.05 level of significance for
the given sample data. Detemine the P-value for this hypothesis
test.
(Round to three decimal places as needed.)
(b) Construct a 95% confidence interval about μ1−μ2.
Population 1
Population 2
n
14
14
x
11.2
8.4
s
2.8
3.2
2, Use the given statistics to complete parts (a) and (b).
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(a) Test whether μ1>μ2...
Assume that both populations are normally distributed. a) Test whether μ1 > μ2 at the alpha...
Assume that both populations are normally distributed. a) Test
whether μ1 > μ2 at the alpha equals 0.05
level of significance for the given sample data. b) Construct a
95% confidence interval about μ1 - μ2. C)
Determine the test statistic
Sample 1
Sample 2
n
22
14
x overbar
50.9
42.6
s
7.3
11.7
Assume that both populations are normally distributed. (a) Test whether mu 1 not equals mu 2μ1≠μ2...
Assume that both populations are normally distributed.
(a) Test whether
mu 1 not equals mu 2μ1≠μ2
at the
alpha equals 0.01α=0.01
level of significance for the given sample data.(b) Construct a
99%
confidence interval about
mu 1 minus mu 2μ1−μ2.
Population 1
Population 2
n
13
13
x overbarx
13.9
11.2
s
3.1
2.8
Assume that both populations are normally distributed. (a) Test whether mu 1 not equals mu 2μ1≠μ2...
Assume that both populations are normally distributed.
(a) Test whether
mu 1 not equals mu 2μ1≠μ2
at the
alpha equals 0.01α=0.01
level of significance for the given sample data.
Population 1
Population 2
n
17
17
x bar
14.614.6
19.819.8
s
4.24.2
3.73.7
Determine the P-value for this hypothesis test.
P=?(Round to three decimal places as needed.)
Test the given claim using the α=0.05 significance level and assuming that the populations are normally...
Test the given claim using the α=0.05 significance level and
assuming that the populations are normally distributed and that the
population variances are equal.
Claim: The treatment population and the placebo population have the
same means.
Treatment group: n=9, x¯=110, s=5.9.
Placebo group: n=7, x¯=116,s=5.7.
The test statistic is =___________
The positive critical value is =__________
The negative critical value is =________
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Ha:μ1>μ2
You believe both populations are normally distributed, but you
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Ho:μ1=μ2Ho:μ1=μ2
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You believe both populations are normally distributed, but you do
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You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1>μ2Ha:μ1>μ2
You obtain the following two samples of data.
Sample #1
Sample #2
67.8
100.5
96.8
59.4
66.7
86.2
89.2
86.7
70.6
100.5
65.8
77.4
78.4
71.9
69.3
61.4
69.6
81.6
90.4
75.3
83.4
70.9
84.5
75.3
62
58.6
77.4
73.8
70.6
83
83
63.6
76.2
61.4
75.6
84.5
92.6
87.6
73.9
77.3
77.8
64.9
67.5
49.7
87
56.5
96.1
75.8
84.1
39.6
63.8
68.5...
Assume that you plan to use a significance level of α = 0.05 to test 5)...
Assume that you plan to use a significance level of α = 0.05 to
test 5)
the claim that p1 = p2. Use the given sample sizes and numbers
of
successes to find the P-value for the hypothesis test, and make
a conclusion addressed to the claim.
n1=100 n2=100
x1 = 38 x2 = 40
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