Answer:
Null hypothesis be H₀ : μ = 100
Alternative hypothesis Hₐ : μ < 100
There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100
Step-by-step explanation:
Here we have;
Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100
Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level
Proposed average location in Wade Tract, μ = 100
Sample mean, = 99.74
Standard deviation, s = 58
Sample size, n = 584
The t test formula is therefore;
Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025
We have = -1.65
Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;
There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.