Question

In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pound per acre.

Control:	2	4	3	4	2	3	3	5	3	2	6	3
Treatment:	0	1	1	2	1	2	1	1	2	1	1	1

Is there significant evidence at the 1% level that the mean number of larvae per stem is reduced by Malathion? Carry out a complete test.

Answer 1

ANSWER::

Here, we are to test,

where,



or, equivalently, to test,

where,


The test statistic is given by:

Under H0,

where,











We reject H0 at level iff

where,


Now,


Also,


Now,


Hence, H0 is rejected at 1% level of significance. That is, there is significanct evidence that the treatment is effective. Or, in other words, Malathion at 0.25 pounds per acre has reduced mean level of larvae.

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