Question

1 Consider the following summary data on the modulus of elasticity ( 105 psi) for lumber of three different grades. Grades 1.64 0.21 2 1.54 0.23 3 71.42 0.22 Use this data and a significance level of 0.01 to test the null hypothesis of no difference in mean modulus of elasticity for the three grades. Calculate the test statistic. (Round your answer to two decimal places.) What can be said about the P-value for the test? OP-value > 0.100 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 What can you conclude? Reject Ho. At least two of the three grades appear to differ significantly, O Reject Ho. The three grades do not appear to differ significantly Fail to reject Ho. The three grades do not appear to differ significantly Fail to reject Ho At least two of the three grades appear to differ significantly

Answer 1

Hypothesis:

H0: all means are same

Ha: Not all means are same

Test:

Treatment	n	X bar	s		n*(X bar - Overall X bar)^2	(n-1)*S^2
Aerobic training	7	1.64	0.21		0.079644444	0.2646
Resistance training	7	1.54	0.23		0.000311111	0.3174
Aerobic plus resistance training	7	1.42	0.22		0.089911111	0.2904
Total	21			Total	0.169866667	0.8724
k	3
Overall X bar	1.533333333
	SS	df	MS	F	Significance F
Groups	0.169866667	2	0.084933	1.752407	0.201665346
Error	0.8724	18	0.048467
Total	1.042266667	20
	SS	df	MS	F
Groups	SUM(n*(X bar - Overall X bar)^2)	k-1	SSG/dfG	MSG/MSE
Error	SUM((n-1)*S^2)	n-k	SSE/dfE
Total	SSG+SSE	n-1

F stat = 1.75

P value = 0.2017

P value > 0.100, Do not reject H0

Fail to reject Ho. The three grades do not appear to differ significantly,