Answer to Question #113900 in Statistics and Probability for Mateus Michael Ndinomwene

Question

1. We are interested to know whether test animals respond to temperature by moving
toward a favoured temperature. Animals were placed in a temperature gradient marked
in units from zero (the starting point) in the middle of the gradient to positive at the
warm end and negative at the cold end. The mean position along the gradient was found
to be -1.352 units, the standard deviation was 12.267 units and n=500 individuals. Is
there a significant tendency to aggregate at either the cold or warm end of the gradient?
Start by setting up a null hypothesis in terms of the mean position along the gradient =
0.

Answer 1

$H_0: \mu=0\\ H_1:\mu \neq 0\\ Let \; \alpha =0.05\implies Z_{\frac{α}{2}}=Z_{\frac{0.05}{2}}=Z_{0.025}=1.96,\\ Z=\frac{\bar x-\mu_0}{\frac{s}{\sqrt n}}\\ Z=\frac{-1.352-0}{\frac{12.267}{\sqrt 500}}=-2.464\\ \text{the rejection region} :\;z>1.96, z<-1.96\\ \text{The decision is to reject}:\; H_0\\ \text{this means that there a significant tendency }\\ \text{to aggregate at either the cold or warm }$