Eason believes that the higher the educational achievement of a mans father, the

Question

Eason believes that the higher the educational achievement of a mans father, the higher his education level. so he went online to check some published survey data. He divided the samples into two groups

Formulate the hypothesis testing using significance level 0.02 and test it. Does the survey provide sufficient evidence that what Eason believes is true?

- please go through all steps necessary, don't use excel

Group #1 : Father has some college education or more Group #2: Father has a high school degree or less And he found a variable which is the number of years of education that each son possesses. The survey shows that Sample size Group #1 Group #2 Mean 15.24 12.57 Std dev 2.56 3.13 359 3

Explanation / Answer

Given that,
mean(x)=15.24
standard deviation , s.d1=2.56
number(n1)=90
y(mean)=12.57
standard deviation, s.d2 =3.13
number(n2)=359
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.02
from standard normal table,right tailed t /2 =2.084
since our test is right-tailed
reject Ho, if to > 2.084
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =15.24-12.57/sqrt((6.5536/90)+(9.7969/359))
to =8.4388
| to | =8.4388
critical value
the value of |t | with min (n1-1, n2-1) i.e 89 d.f is 2.084
we got |to| = 8.43876 & | t | = 2.084
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 8.4388 ) = 0
hence value of p0.02 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 8.4388
critical value: 2.084
decision: reject Ho
p-value: 0

the higher the educational achievement of a mans father, the higher his education level

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