Question

Problem 6 During each of four experiments on the use of carbon tetrachloride as a worm killer, ten rats were infested with larvae (Armitage 1983). Eight days later, five rats were treated with car- bon tetrachloride; the other five were kept as controls. After two more days, all the rats were killed and the numbers of worms were counted. Significant differences, although not expected, might be attributable to changes in experimental conditions. A finding of significant differences could result in more carefully controlled experimentation and thus greater preci- sion in later work A partial ANOVA table for these data follows: Source de Ss MSS Brand 9078.067 Error Total 91187.8 (a) Fill in the missing entries in the ANOVA table. (b) State the null and altemative hypothesis of interest in this experiment. (c) Use x = 0.1 to carry out the hypothesis test in part (b). [6] [2] [6] Answer: Your answer here

Answer 1

Answer:-

Given that:-

Source	df	ss	Mss	F
Brand	5-1=4	36312.268	9078.067	0.82715
Error	10-5=5	54875.532	10975.1064
Total	10-1=9	91187.8

(a) The given problem there are total 10 eats,

i.e., N=10 & no.of treatments f=5

hence brand carriers 4 d.f & there are 9 total d.f

Now, to find sum of savares (ss) we use mss, i.e., $MSS=\frac{SS}{dF}\Rightarrow SS=MSS\times d.F$

For error SS

Total SS= treatement SS+Error 8S

Error SS=Total SS- treatement 8S

F mass of treatment mass of Error + Ft-1,N-1,0

(b) treatement effects are insignificant V/s

Но

$H_{1}:$ treatement effects are siginificant

i.e.,
ai = ak
v/s  $\alpha i\neq \alpha k$ for atleast once $i\neq k$

(c) Test statistic;

F=0.82715

Ftable value = $F_{t-1,N-t,\alpha }$

$=F_{4,5,0.1}$

$=3.520196$

Decision: Here $F<F_{table}$ value

Hence we accept
он
at $\alpha =0.1$

Conclusion:- Treatement given in given problem are insignificant.