Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed.​(a) Test whethermu 1μ1greater than>mu 2μ2at thealphaαequals=0.01level of significance for the given sample data.​(b) Construct a99​%confidence interval aboutmu 1μ1minus−mu 2μ2.  Population 1Population 2 n2425x overbarx50.845.9s4.311.4​(a) Identify the null and alternative hypotheses for this test.  A.H0​:mu 1μ1greater than>mu 2μ2H1​:mu 1μ1equals=mu 2μ2 B.H0​:mu 1μ1equals=mu 2μ2H1​:mu 1μ1less than<mu 2μ2 C.H0​:mu 1μ1less than<mu 2μ2H1​:mu 1μ1equals=mu 2μ2 D.H0​:mu 1μ1not equals≠mu 2μ2H1​:mu 1μ1equals=mu 2μ2 E.H0​:mu 1μ1equals=mu 2μ2H1​:mu 1μ1greater than>mu 2μ2 F.H0​:mu 1μ1equals=mu 2μ2H1​:mu 1μ1not equals≠mu 2μ2 Find the test statistic for this hypothesis test.  ​(Round to two decimal places as​ needed.)

Question
Asked Nov 23, 2019
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Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed.
​(a) Test whether
mu 1μ1greater than>mu 2μ2
at the
alphaαequals=0.01
level of significance for the given sample data.
​(b) Construct a
99​%
confidence interval about
mu 1μ1minus−mu 2μ2.
 
 
Population 1
Population 2
 
n
24
25
x overbarx
50.8
45.9
s
4.3
11.4
​(a) Identify the null and alternative hypotheses for this test.
 
 
A.
H0​:
mu 1μ1greater than>mu 2μ2
H1​:
mu 1μ1equals=mu 2μ2
 
B.
H0​:
mu 1μ1equals=mu 2μ2
H1​:
mu 1μ1less than<mu 2μ2
 
C.
H0​:
mu 1μ1less than<mu 2μ2
H1​:
mu 1μ1equals=mu 2μ2
 
D.
H0​:
mu 1μ1not equals≠mu 2μ2
H1​:
mu 1μ1equals=mu 2μ2
 
E.
H0​:
mu 1μ1equals=mu 2μ2
H1​:
mu 1μ1greater than>mu 2μ2
 
F.
H0​:
mu 1μ1equals=mu 2μ2
H1​:
mu 1μ1not equals≠mu 2μ2
 
Find the test statistic for this hypothesis test.
 
 
​(Round to two decimal places as​ needed.)
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Expert Answer

Step 1

The provided information are:

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n=24 25 50.8 45.9 4.3 11.4

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Step 2

(a)

The null and alternative hypotheses are:

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Ho i< \ri : °H

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Step 3

Hence, the correct option is (E).

The alternative hypothesis suggests that the t...

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т -х, - (4 - м,) 1 = 1 п, п, where ( -1)s + (п, -1)5, п+п, -2 с8

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