The Excel display below shows the results of a one-way analysis of variance. Ass

Question

The Excel display below shows the results of a one-way analysis of variance. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. What can you conclude about the equality of the population means?

-Reject the null hypothesis since the P-value is greater than the significance level.

-Reject the null hypothesis since the P-value is less than the significance level.

-Fail to reject the null hypothesis since the P-value is less than the significance level.

-Fail to reject the null hypothesis since the P-value is greater than the significance level.

Explanation / Answer

Assume values of given data
mean(x)=0.77
standard deviation , 1 =0.2
number(n1)=40
y(mean)=0.77
standard deviation, 2 =0.3
number(n2)=50
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=0.77-0.77/sqrt((0.04/40)+(0.09/50))
zo =0
| zo | =0
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =0 & | z | =1.96
make decision
hence value of | zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0 ) = 1
hence value of p0.05 < 1,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: 0
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 1
Fail to reject the null hypothesis since the P-value is greater than the significance level

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