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   136
129   137   139
132   137   141
135   129   142
132   136   137
134   138   145
138   134   137

1.Find the​ P-value.

The​ P-value is____

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

2.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

Answer:

Based on the given data:

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

Claim to test: Use a 0.05 significance level to test the claim that the different epochs all have the same mean.

Null Hypothesis: $H_0: \mu_1 = \mu_2 = \mu_3$

Alternate Hypothesis: $H_a$ ; Not all means are equal

One Way ANOVA test can be performed to test the claim:

Anova Summary	Treatments
	1	2	3	Total
N	9	9	9	27
∑X	1194	1210	1243	3647
Mean	132.7	134.4	138.1	135.1
∑X2	158544	162768	171853	493165
Std.Dev.	4.18	3.36	4.76	4.60

Source	SS	df	MS
Between	138.741	2	69.37
Within	411.111	24	17.13
Total	549.852	26

F	Fcritical	p-value
4.0497	3.4028	0.0305

F-Value for One way ANOVA test is 4.0497 and p-value is 0.0305

Since p-value (0.0305) is < significance level (0.05), therefore, Null Hypothesis is rejected.

Their is not sufficient evidence to claim that the different epochs all have the same mean.

1.Find the​ P-value.

• The​ P-value is 0.031 ​(Round to three decimal places as​ needed.)

2.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 - Correct Option