Question

4. A test (?-0.025) is conducted to determine if there is a difference between the GPA. of psychology majors and math majors. A sample of 36 psychology majors resulted in yi - 3.2 and si -0.4. A sample of 40 math majors resulted in 2 3.0 and s2-0.3. (a) State the null and alternative hypothesis. (b) Give the rejection region. (c) Determine the test value and state the conclusion. (d) Find the P-value. (e) State the conclusion if ?-001. Use the Satterthwaite formula for the degrees of freedom.

Answer 1

4.

Given that,
mean(x)=3.2
standard deviation , s.d1=0.4
number(n1)=36
y(mean)=3
standard deviation, s.d2 =0.3
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, ? = 0.025
from standard normal table, two tailed t ?/2 =2.342
since our test is two-tailed
reject Ho, if to < -2.342 OR if to > 2.342
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =3.2-3/sqrt((0.16/36)+(0.09/40))
to =2.444
| to | =2.444
critical value
the value of |t ?| with min (n1-1, n2-1) i.e 35 d.f is 2.342
we got |to| = 2.4444 & | t ? | = 2.342
make decision
hence value of | to | > | t ?| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.4444 ) = 0.02
hence value of p0.025 > 0.02,here we reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
c.
test statistic: 2.444
critical value: -2.342 , 2.342
b.
decision: reject Ho
d.
p-value: 0.02
we have enough evidence to support the claim that difference between GPa of psychology majors and math majors
e.
Given that,
mean(x)=3.2
standard deviation , s.d1=0.4
number(n1)=36
y(mean)=3
standard deviation, s.d2 =0.3
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, ? = 0.01
from standard normal table, two tailed t ?/2 =2.724
since our test is two-tailed
reject Ho, if to < -2.724 OR if to > 2.724
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =3.2-3/sqrt((0.16/36)+(0.09/40))
to =2.444
| to | =2.444
critical value
the value of |t ?| with min (n1-1, n2-1) i.e 35 d.f is 2.724
we got |to| = 2.4444 & | t ? | = 2.724
make decision
hence value of |to | < | t ? | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.4444 ) = 0.02
hence value of p0.01 < 0.02,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.444
critical value: -2.724 , 2.724
decision: do not reject Ho
p-value: 0.02
we do not have enough evidence to support the claim that difference between GPa of psychology majors and math majors

sattethrwaite formula for degree of freedom
df =(S1^2/n1 -S2^2/n2)^2/((1/n1-1)*(S1^2/n1)^2 +(1/n2-1)*(S2^2/n2)^2)
df = ((0.4^2/36)-(0.3^2/40))^2/((1/35)*(0.16/36)^2+(1/39)*(0.09/40)^2)
df = 6.937