In a study designed to test whether there is a difference between the average he
ID: 3314281 • Letter: I
Question
In a study designed to test whether there is a difference between the average heights of adult females born in Korea and Japan; random samples yielded the following results: sample size 120 150 Average height in inches 62.7 61.8 Standard deviation in inches 2.50 2.62 Korea Japan (a) Use critical region approach to test the null hypothesis that the corresponding popu lation averages are equal against the alternative hypothesis that they are not equal, at the level of significance 0.05. State clearly the hypotheses, test statistic, critical 10 marks (b) Find the p-value for part (a). Hence, determine whether the ull hypothesis is rejected 5 marks region and conclusion. at 0.01 significance level.Explanation / Answer
PART A.
Given that,
mean(x)=62.7
standard deviation , s.d1=2.5
number(n1)=120
y(mean)=61.8
standard deviation, s.d2 =2.62
number(n2)=150
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =1.98
since our test is two-tailed
reject Ho, if to < -1.98 OR if to > 1.98
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =62.7-61.8/sqrt((6.25/120)+(6.8644/150))
to =2.8772
| to | =2.8772
critical value
the value of |t | with min (n1-1, n2-1) i.e 119 d.f is 1.98
we got |to| = 2.87721 & | t | = 1.98
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.8772 ) = 0.005
hence value of p0.05 > 0.005,here we reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.8772
critical value: -1.98 , 1.98
decision: reject Ho
p-value: 0.005
there is difference between the average heights of adult females born in korea and japan
PART B.
AT 0.01 LOS
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.8772 ) = 0.005
hence value of p0.01 > 0.005,here we reject Ho