Question

Pesticides sprayed on crops can affect human beings. A symptom of the action of a pesticide is reduction

in brain acetylcholinesterase (AChE) activity, and a severe reduction can be dangerous in terms of body

functions. When cotton is sprayed, one criterion of the existence of such a reduction is whether quail in

field borders show reduced AChE activity. In one collection, the following six observations were made

for brain AChE activity in quail: 86.03, 83.67, 95.21, 92.94, 83.12 and 80.22. Suppose that the mean

brain AChE activity for quail who have not been exposed to the pesticide is 95. Do these data show a

reduction in AChE activity. Test at a 0.05 significance level

Answer 1

there is sufficient evidence of these data show a reduction in AChE activity.

here we want to test the null hypothesis H0:=95 and alternate hypothesis Ha:<95,

since population standard deviation is not given, so we use t-test and

statistic t=(-)/(s/)=(86.87-95)/(5.93/(sqrt(6)))=-3.36 with n-1=6-1=5 df

this is one tailed test and one tailed critical t(0.05,5)=2.02 is less than absolute value of the calculated/observed t=3.36, so we fail to accept (or reject ) null hypothesis and conclude that there is sufficient evidence of these data show a reduction in AChE activity.

s.n.	x
1	86.03
2	83.67
3	95.21
4	92.94
5	83.12
6	80.22
x-bar=	86.87
s=	5.93
n=	6
t=	-3.36
one tailed critical t(0.05,5)=	2.02