Test whether mu 1 less than mu 21<2 at the alphaequals=0.010.01 level of signifi
ID: 3289375 • Letter: T
Question
Test whether
mu 1 less than mu 21<2
at the
alphaequals=0.010.01
level of significance for the sample data shown in the accompanying table. Assume that the populations are normally distributed.
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Population 1
Population 2
n
3333
2525
x overbarx
103.4103.4
114.5114.5
s
12.312.3
13.213.2
Determine the null and alternative hypothesis for this test.
A.
Upper H 0 :H0:mu 1 equals mu 21=2
Upper H 1 :H1:mu 1 not equals mu 212
B.
Upper H 0 :H0:mu 1 less than mu 21<2
Upper H 1 :H1:mu 1 equals mu 21=2
C.
Upper H 0 :H0:mu 1 equals mu 21=2
Upper H 1 :H1:mu 1 less than mu 21<2
D.
Upper H 0 :H0:mu 1 not equals mu 212
Upper H 1 :H1:mu 1 less than mu 21<2
Detemine the P-value for this hypothesis test.
Pequals=nothing
(Round to three decimal places as needed.)
State the appropriate conclusion. Choose the correct answer below.
A.
Do not rejectDo not reject
Upper H 0H0.
There
is notis not
sufficient evidence at the
alphaequals=0.010.01
level of significance to conclude that mu 1 less than mu 2 .1<2.
B.
RejectReject
Upper H 0H0.
There
isis
sufficient evidence at the
alphaequals=0.010.01
level of significance to conclude that mu 1 less than mu 2 .1<2.
C.
Do not rejectDo not reject
Upper H 0H0.
There
isis
sufficient evidence at the
alphaequals=0.010.01
level of significance to conclude that mu 1 less than mu 2 .1<2.
D.
RejectReject
Upper H 0H0.
There
is notis not
sufficient evidence at the
alphaequals=0.010.01
level of significance to conclude that mu 1 less than mu 2 .
Explanation / Answer
(first part) Determine the null and alternative hypothesis for this test.
right choice is
C. H 0 :1=2
H 1 1<2
(second) Detemine the P-value for this hypothesis test.
here we use t-test and
t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2
(third part) State the appropriate conclusion. Choose the correct answer below.
since p-value=0.000954 is less than alpha=0.01 so we reject H0 and conclude that
There is sufficient evidence at alpha=0.01 level of significance to conclude that .1<2.
sample mean s s2 n (n-1)s2 population1 103.4 12.3 151.29 33 4841.28 population2 114.5 13.2 174.24 25 4181.76 total 325.53 58 9023.04 sp2= 161.1257 sp= 12.69353 t= -3.298022 one tailed p-value= 0.000954Related Questions
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