Question

The values in the table below are measured maximum breadths​ (in millimeters) of male skulls from different epochs. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 significance level to test the claim that the different epochs all have the same mean.

4000 B.C	1850 B.C.	150 A.D.
131	129	128
138	134	138
125	136	138
129	137	139
132	137	141
135	130	142
132	136	136
134	138	145
140	134	137

Find the​ P-value.

The​ P-value is____?

​(Round to three decimal places as​ needed.)

Test the claim that the different epochs all have the same mean.

A.

There is sufficient evidence to reject the claim that the different epochs have the same mean.

B.

There is not sufficient evidence to reject the claim that the different epochs have the same mean.

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
4000 B.C	9	1196	132.8889	20.61111
1850 B.C.	9	1211	134.5556	10.02778
150 A.D.	9	1244	138.2222	22.44444
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	134	2	67	3.786499	0.037217	3.402826
Within Groups	424.6667	24	17.69444
Total	558.6667	26

So from the above output

• The​ P-value is 0.037

P value < l.o.s

i.e., 0.037 < 0.05

so reject H0

Conclusion:

• There is sufficient evidence to reject the claim that the different epochs have the same mean.