Consider the following hypothesis statement using alphaequals=0.01 and data from
ID: 3358400 • Letter: C
Question
Consider the following hypothesis statement using
alphaequals=0.01
and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts a and b.
Upper H 0 : mu 1 minus mu 2 equals 0H0: 12=0
x overbar 1 equals 14.3
x overbar 2 equals 13.0
Upper H 1 : mu 1 minus mu 2 not equals 0H1: 120
s 1 equals 2.7
s 2 equals 3.2
n1=22
n2=15
a. Calculate the appropriate test statistic and interpret the result.
The test statistic is
nothing.
(Round to two decimal places as needed.)
What are the critical values? round to three decimals
b. What is the P value? round to three decimals
Upper H 0 : mu 1 minus mu 2 equals 0H0: 12=0
x overbar 1 equals 14.3
x overbar 2 equals 13.0
Upper H 1 : mu 1 minus mu 2 not equals 0H1: 120
s 1 equals 2.7
s 2 equals 3.2
n1=22
n2=15
Explanation / Answer
Given that,
mean(x)=14.3
standard deviation , s.d1=2.7
number(n1)=22
y(mean)=13
standard deviation, s.d2 =3.2
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.01
from standard normal table, two tailed t /2 =2.98
since our test is two-tailed
reject Ho, if to < -2.98 OR if to > 2.98
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =14.3-13/sqrt((7.29/22)+(10.24/15))
to =1.291
| to | =1.291
critical value
the value of |t | with min (n1-1, n2-1) i.e 14 d.f is 2.98
we got |to| = 1.29098 & | t | = 2.98
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.291 ) = 0.218
hence value of p0.01 < 0.218,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.291 = 1.29
critical value: -2.98 , 2.98
b.
decision: do not reject Ho
p-value: 0.218
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