Question

To study the relationship between hair colour (dark or light) and eye colour (dark or light) in a German population, an anthropologist observed a sample of 6800 men. Is eye colour associated with hair colour?

Determine the following for the given scenarios:
1. Kind of hypothesis test to be conducted
2. Null and alternative hypotheses
3. Test statistic to be calculated

Answer 1

To study the relationship between hair colour (dark or light) and eye colour (dark or light)
in a German population

Assumed values,
mean(x)=3100
standard deviation , sigma1 =420
number(n1)=6800
y(mean)=2750
standard deviation, sigma2 =425
number(n2)=6800
null, Ho: u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=3100-2750/sqrt((176400/6800)+(180625/6800))
zo =48.303
| zo | =48.303
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo | =48.303 & | z alpha | =1.96
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 48.303 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
1.
t test for difference of means
2.
null, Ho: u1 = u2
3.
alternate, H1: μ1 != u2
test statistic: 48.303
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that eye colour associated with hair colour