Researchers measured skulls from different time periods in an attempt to determi

Question

Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below (based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver, Oxford University Press). Use a 0.05 significance level to test the claim that that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. Assume that both samples are independent simple random samples from populations having normal distributions

a)find test statistic

b)find upper critical f value between 2 numbers

c)find p value

d)reject or fail to reject

4000 B.C (max skull breadth) n=30 x=131.37mm s=5.13mm 150 A.D (max skull breadth) n=30 x=136.17mm s=5.35mm

Explanation / Answer

Answer to the question)

Claim is that the two groups have same Variance

The test statistics is F = s1^2 / s2^2

F = (5.35)^2 / (5.15)^2

F = 1.0792

Df n = 30-1 = 29

df d = 30-1 = 29

At alpha = 0.05

the F critical value is : 1.8608

.

P value is : 0.4194 ...[used excel command =f.dist.rt(1.0792,29,29) to get the P value ]

.

Since the P value is greater than alpha 0.05 , we FAIL to reject the Null

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