A random sample of 9 observations from one population revealed a sample mean of
ID: 3317233 • Letter: A
Question
A random sample of 9 observations from one population revealed a sample mean of 25 and a sample standard deviation of 4.0. A random sample of 4 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.6.
State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)
Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
The null and alternate hypotheses are: H0 : 1 = 2 H1 : 1 2A random sample of 9 observations from one population revealed a sample mean of 25 and a sample standard deviation of 4.0. A random sample of 4 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.6.
Explanation / Answer
Given that,
mean(x)=25
standard deviation , s.d1=4
number(n1)=9
y(mean)=29
standard deviation, s.d2 =4.6
number(n2)=4
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.01
from standard normal table, two tailed t /2 =3.11
since our test is two-tailed
reject Ho, if to < -3.11 OR if to > 3.11
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (8*16 + 3*21.16) / (13- 2 )
s^2 = 17.4073
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=25-29/sqrt((17.4073( 1 /9+ 1/4 ))
to=-4/2.5072
to=-1.5954
| to | =1.5954
critical value
the value of |t | with (n1+n2-2) i.e 11 d.f is 3.11
we got |to| = 1.5954 & | t | = 3.11
ANSWERS
---------------
a.
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != -1.5954 ) = 0.1366
hence value of p0.01 < 0.1366,here we do not reject Ho
b.
pooled variance s^2 = 17.4073
c.
test statistic: -1.5954
null, Ho: u1 = u2
alternate, H1: u1 != u2
critical value: -3.11 , 3.11
d.
decision: do not reject Ho
e.
p-value: 0.1366
conclusion:
we don't have evidence to say that there a difference between the population means
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