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 3 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).
Assume that the populations are normally distributed.
(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 =________
Is there sufficient evidence to warrant the rejection of the claim
that the treatment and placebo populations have...
You wish to test the following claim (HaHa) at a significance level of α=0.05 Ho:μ1=μ2 Ha:μ1>μ2...
You wish to test the following claim (HaHa) at a significance
level of α=0.05
Ho:μ1=μ2
Ha:μ1>μ2
You believe both populations are normally distributed, but you
do not know the standard deviations for either. And you have no
reason to believe the variances of the two populations are equal
You obtain a sample of size n1=23n1=23 with a mean of ¯x1=73.1x and
a standard deviation of s1=15.5 from the first population. You
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Test at the α = 0.05 significance level whether the mean of a
random sample of size n = 16 is statistically significantly less
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normal, ?̅= 8.4 and ? 2 = 10.24. a) What is the appropriate test
you can use to test the claim? b) What are the null and alternative
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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 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 believe both populations are normally distributed, but you do
not know the standard deviations for either. However, you also have
no reason to believe the variances of the two populations are not
equal. You obtain a sample of size n1=12n1=12 with a mean of
M1=71.3M1=71.3 and a standard deviation of SD1=11.6SD1=11.6 from
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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 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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