Question

Create a case on the application of inferences about the difference between two population means (σ1 and σ2 known) and explain the hypothesis tests until conclusion.

Answer 1

Suppose we want to study the number of cavity trees in old growth stands in Adirondack Park in northern New York. We wants to know if there is a significant difference between the mean number of cavity trees in the Adirondack Park and the old growth stands in the Monongahela National Forest.The average of 46 stands is 39.6 and a standard deviation is 9.4 and second the average of 50 stands is 43.9 with standard deviation 10.7. We use a 5% level of significance to test this claim.

Hypothesis:

Ho: There is a no significant difference between the mean number of cavity trees in the Adirondack Park and the old growth stands in the Monongahela National Forest.

i.e.

V/s

H1: There is a significant difference between the mean number of cavity trees in the Adirondack Park and the old growth stands in the Monongahela National Forest.

i.e.

Test statistic :

Here we have given that (σ1 and σ2 known) then we use normal test statistic.

Under Ho,

Decision: If Calculated Z > Zcritical at 0.05 level of significance then we reject Ho.

Also from p-value,

If p-value < alpha = 0.05 then we reject Ho.