We have just conducted a study comparing cognitive development of low and normal

Question

We have just conducted a study comparing cognitive development of low and normal-birthweight babies who have reached 1 year of age. Using a scale we devised, we found that the sample means of the two groups were 25 and 30, respectively, with a pooled standard deviation of 8. Assume that we wish to replicate this experiment with 20 subjects in each group. If we assume that the true means and standard deviations have been estimated exactly, what is the a priori probability that we will find a significant difference in our replication?

Explanation / Answer

Given that,
mean(x)=25
standard deviation , s.d1=8
number(n1)=20
y(mean)=30
standard deviation, s.d2 =8
number(n2)=20
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.024
since our test is two-tailed
reject Ho, if to < -2.024 OR if to > 2.024
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (19*64 + 19*64) / (40- 2 )
s^2 = 64
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=25-30/sqrt((64( 1 /20+ 1/20 ))
to=-5/2.53
to=-1.976
| to | =1.976
critical value
the value of |t | with (n1+n2-2) i.e 38 d.f is 2.024
we got |to| = 1.976 & | t | = 2.024
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != -1.9764 ) = 0.0552
hence value of p0.05 < 0.0552,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -1.976
critical value: -2.024 , 2.024
decision: do not reject Ho
p-value: 0.0552

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