Question

Aging workers of the Neotropical termite, Neocapritermes taracua, develop blue crystal containing glands ("backpacks") on their backs, When they fight intruding termites and are hampered, these "blue" termites explode, and the glands spew a sticky liquid (Sobotnik et al. 2012). The following data are from an experiment that measured the toxicity of the blue substance. A single drop of the liquid extracted from blue termites was placed on individuals of a second termite species, Labiotermes labralis, and the number that were immobilized (dead or paralyzed) within 60 minutes was recorded. The frequency of this outcome was compared with a control treatment in which liquid from glands of "white" termites lacking the blue crystals was dropped instead.

Is the blue liquid toxic compared to liquid from white termites?
Liquid source Unharmed Immobilized
Blue workers 3 37
White workers 31 9

Answer 1

The blue liquid is toxic

Explanation:

From the calculations I have done and attached to this problem

Null hypothesis:

H0 : p1 <= p2

Alternate hypothesis:

H1 : p1 > p2

^p1 = 0.925

^p2 = 0.2250

^P = (x1 + x2)/(n1+n2)

= 0.575

After calculating, I got test statistics = 6.33 ( check attachment)

P(z > 6.33) = 0.0000

In conclusion, our pvalue has been found to be less than the level of significance 0.05 so we reject null hypothesis and accept that we have enough sample evidence that the blue liquid is more toxic in comparison to white one.

Please check attachment for calculated test statistics.