Means difference testing homework problems Starting data set: Mean 45.25 47.50 S
ID: 3332088 • Letter: M
Question
Means difference testing homework problems
Starting data set:
Mean 45.25 47.50
Std dev 2.15 2.46
n 8 8
1. Is there a statistical difference between the means (for the starting data set)?
2. What if there were 10 values in each group (rather than the original 8 in each group)?
3. What if there were 25 values in each group (rather than the original 8 in each group)?
4. What if you had n = 25 in both groups AND the standard deviation increased to 4.5 for both groups?
Explanation / Answer
Q1.
Given that,
mean(x)=45.25
standard deviation , s.d1=2.15
number(n1)=8
y(mean)=47.5
standard deviation, s.d2 =2.46
number(n2)=8
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.365
since our test is two-tailed
reject Ho, if to < -2.365 OR if to > 2.365
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =45.25-47.5/sqrt((4.6225/8)+(6.0516/8))
to =-1.948
| to | =1.948
critical value
the value of |t | with min (n1-1, n2-1) i.e 7 d.f is 2.365
we got |to| = 1.94788 & | t | = 2.365
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.9479 ) = 0.092
hence value of p0.05 < 0.092,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -1.948
critical value: -2.365 , 2.365
decision: do not reject Ho
p-value: 0.092
decision is, no statistical difference between the meanss
Q2.
number(n1)=10
number(n2)=10
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =45.25-47.5/sqrt((4.6225/10)+(6.0516/10))
to =-2.178
| to | =2.178
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 2.262
we got |to| = 2.17779 & | t | = 2.262
make decision
hence value of |to | < | t | and here we do not reject Ho
decision is, no statistical difference between the means
Q3.
number(n1)=25
number(n2)=25
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =45.25-47.5/sqrt((4.6225/25)+(6.0516/25))
to =-3.443
| to | =3.443
critical value
the value of |t | with min (n1-1, n2-1) i.e 24 d.f is 2.064
we got |to| = 3.4434 & | t | = 2.064
make decision
hence value of | to | > | t | and here we reject Ho
decision is, statistical difference between the means
Q4.
standard deviation , s.d1=4.5
number(n1)=25
standard deviation, s.d2 =4.5
number(n2)=25
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =45.25-47.5/sqrt((20.25/25)+(20.25/25))
to =-1.768
| to | =1.768
critical value
the value of |t | with min (n1-1, n2-1) i.e 24 d.f is 2.064
we got |to| = 1.76777 & | t | = 2.064
make decision
hence value of |to | < | t | and here we do not reject Ho
decision: do not reject Ho
decision is, no statistical difference between the means