alphaequals=0.05 Upper H 0 : mu 1 minus mu 2 equals 0H0: 12=0 Upper H 1 : mu 1 m
ID: 3358936 • Letter: A
Question
alphaequals=0.05
Upper H 0 : mu 1 minus mu 2 equals 0H0: 12=0
Upper H 1 : mu 1 minus mu 2 not equals 0H1: 120
a) Calculate the appropriate test statistic and interpret the result.
b) Calculate the p-value and interpret the result.
x overbarx1
equals=
200
x overbarx2
equals=
180
sigma1
equals=
48
sigma2
equals=
63
n1
equals=
43
n2
equals=
35
nbsp
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a) The test statistic is
nothing.
(Round to two decimal places as needed.)
Determine the appropriate critical value(s). Select the correct choice below and fill in the answer box to complete your answer.
(Round to
twotwo
decimal places as needed.)
A.
The critical value is
nothing.
B.
The critical values are
plus or minus±nothing.
Since the test statistic
does not fall
falls
in the rejection region,
do not reject
reject
Upper H 0H0.
There is
sufficient
insufficient
evidence to conclude that the mean of population 1 is different from the mean of population 2.b) The p-value is
nothing.
(Round to three decimal places as needed.)
Since the p-value is
equal to
greater than
less than
alpha,
reject
do not reject
Upper H 0H0.
There is
insufficient
sufficient
evidence to conclude that the mean of population 1 is different from the mean of population 2.
Consider the hypothesis statement shown below usingalphaequals=0.05
and the data to the right from two independent samples.Upper H 0 : mu 1 minus mu 2 equals 0H0: 12=0
Upper H 1 : mu 1 minus mu 2 not equals 0H1: 120
a) Calculate the appropriate test statistic and interpret the result.
b) Calculate the p-value and interpret the result.
x overbarx1
equals=
200
x overbarx2
equals=
180
sigma1
equals=
48
sigma2
equals=
63
n1
equals=
43
n2
equals=
35
nbsp
Explanation / Answer
Given that,
mean(x)=200
standard deviation , s.d1=48
number(n1)=43
y(mean)=180
standard deviation, s.d2 =63
number(n2)=35
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.032
since our test is two-tailed
reject Ho, if to < -2.032 OR if to > 2.032
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =200-180/sqrt((2304/43)+(3969/35))
to =1.5477
| to | =1.5477
critical value
the value of |t | with min (n1-1, n2-1) i.e 34 d.f is 2.032
we got |to| = 1.54773 & | t | = 2.032
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.5477 ) = 0.131
hence value of p0.05 < 0.131,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.5477
critical value: -2.032 , 2.032
decision: do not reject Ho
p-value: 0.131
no evidence to conclude that the mean of population 1 is different from the mean of population 2
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