Question

Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are independent simple random samples from populations having normal distributions. Use a

0.05

significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150.

	n	x overbarx	s
4000 B.C.	30	131.36 mm	5.17 mm
A.D. 150	30	136.98 mm	5.34 mm

identify the test statistic, and the p-value,

Answer 1

Null and alternative hypothesis:
Hₒ : σ₁ = σ₂
H₁ : σ₁ ≠ σ₂

Test statistic:  
F = s₁² / s₂² = 5.34² / 5.17² =    1.0668

Degree of freedom:  
df₁ = n₁-1 =    29
df₂ = n₂-1 =    29

P-value :  
P-value = 2*F.DIST.RT(1.0668, 29, 29) =    0.8629

Conclusion:  
As p-value > α, we fail to reject the null hypothesis.  

There is no enough evidence to reject the  claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150.