Consider the following results for two samples randomly taken from two normal po
ID: 3228648 • Letter: C
Question
Consider the following results for two samples randomly taken from two normal populations with equal variances At alpha = 05, is there conclusive evidence that one population has a larger mean? There is enough evidence that sample 1 has a larger mean There is enough evidence that sample 2 has a larger mean There is not enough evidence that either one of population has a larger mean than the other There is enough evidence that the mean amounts from the two populations are the same There is enough evidence that either one of population has a larger mean than the other.Explanation / Answer
Given that,
mean(x)=48
standard deviation , 1 =1.2
number(n1)=28
y(mean)=44
standard deviation, 2 =0.8
number(n2)=35
null, Ho: u1 = u2
alternate, one population has a larger mean valueH1: 1 > u2
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=48-44/sqrt((1.44/28)+(0.64/35))
zo =15.15
| zo | =15.15
critical value
the value of |z | at los 0.05% is 1.645
we got |zo | =15.15 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail -Ha : ( p > 15.15 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate,one population has a larger mean value H1: 1 > u2
test statistic: 15.15
critical value: 1.645
decision: reject Ho
p-value: 0
there is enough evidence that one population has a larger mean value