Question

QUESTION 1 A certain treatment was applied to a set of tree stumps in which a chemical was used with the purpose of regenerating the roots of the stumps. A spray was used with four levels of chemical concentration. After a period of time, the height of the shoots was observed. Perform a one-factor analysis of variance on the data in the accompanying table. Test to see if the concentration of the chemical has a significant impact on the height of the shoots. Use a=0.025. 4 2.80 2.03 3.06 3.15 Chemical Level 1 2 3 2.12 2.77 2.82 2.61 3.12 1.44 1.86 2.09 3.17 3.22 2.94 2.93 What are the hypotheses for this test? Ho: At least two of the Mi's are not equal. HiiH 1 = 2 = 3 = 4 Ho: W1* H2* H3H4 Hi Hi = H2 = H3 = -4 Ho: Mi = H2 = 3 = 4 H : At least two of the Wi's are not equal. Ho: M1 = 2 = 3 = 44 "Hi: At least two of the Mi's are the same. Hoi H1 = H2 = H3 = 4 H1: 41742743744

Answer 1

$Option~C:~H_1:~At~least~two~of~the~\mu_i's~are~not~equal\\\\ H_0:\mu_1=\mu_2=\mu_3=\mu_4\\\\$

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
1	4	9.81	2.4525	0.358492
2	4	10.92	2.73	0.202467
3	4	10.36	2.59	0.609133
4	4	11.04	2.76	0.258867
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.239869	3	0.079956	0.223817	0.878008	4.474185
Within Groups	4.286875	12	0.35724
Total	4.526744	15

Since P-value= 0.878008>0.025, we fail to reject H0 at 2.5% level of significance. Hence we conclude that the concentration of the chemical has not significant impact on the height of the shoots.