(25 points) Some archaeologists theorize that ancient Egyptians interbred with s
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(25 points) Some archaeologists theorize that ancient Egyptians interbred with several immigrant populations over thousands of years. To see if there is any evidence of changes in body structure that might of resulted, they measured 30 skulls of male Egyptians dated from 4000 B . C. E. and 30 others dated from 200 BC. E. The meanandstandard- deviation for the 4000 B.C.E.sample are 131.37 and 5.13, respectively. The mean and standard deviation for the 200 B.C.E. sample are 135.63 and 4.04, respectively. Do the data provide evidence that the mean breadth of male skulls changed over this period? Run the appropriate significance test at the 0.05 level. Assume that the conditions for inference are met. This may help you computationally: SEx.x.-1.192 (4000 ) 139 (20G)Explanation / Answer
Given that,
mean(x)=131.37
standard deviation , s.d1=5.13
number(n1)=30
y(mean)=135.63
standard deviation, s.d2 =4.04
number(n2)=30
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.045
since our test is two-tailed
reject Ho, if to < -2.045 OR if to > 2.045
stanadard error = sqrt(s.d1^2/n1)+(s.d2^2/n2)
where,
sd1, sd2 = standard deviation of both
n1, n2 = sample size
stanadard error = sqrt((26.317/30)+(16.322/30))
= 1.192
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =131.37-135.63/sqrt((26.3169/30)+(16.3216/30))
to =-3.5733
| to | =3.5733
critical value
the value of |t | with min (n1-1, n2-1) i.e 29 d.f is 2.045
we got |to| = 3.5733 & | t | = 2.045
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -3.5733 ) = 0.001
hence value of p0.05 > 0.001,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -3.5733
critical value: -2.045 , 2.045
decision: reject Ho
p-value: 0.001
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