One way to measure whether the trees in the Wade Tract are uniformly distributed is to examine the average location in the north

Question

1 month ago

6

One way to measure whether the trees in the Wade Tract are uniformly distributed is to examine the average location in the north

-south or the east-west direction. The values range from 0 to 200, so if the trees are uniformly distributed, the average location should be 100, and any differences in the actual sample would be due to random chance. The actual sample mean in the north-south direction for the 584 trees in the tract is 99.74. A theoretical calculation for uniform distributions (the details are beyond the scope of this course) gives a standard deviation of 58. Carefully state the null and alternative hypotheses in terms of the true average north-south location. Test your hypotheses by reporting your results along with a short summary of your conclusions.

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-04-08T17:42:19+03:00

Answer:

The null hypothesis is stated as H₀: μ = 100

The alternative hypothesis is Hₐ: μ < 100

Evidence suggests that the average location in Wade Tract is 100

Step-by-step explanation:

We define our null hypothesis as H₀: μ = 100, where the average location of trees in the Wade Tract amounts to 100.

Our alternative hypothesis thereby is stated as Hₐ: μ < 100 at a 95% confidence level.

Proposed average location in Wade Tract is μ = 100.

The sample mean computes to $\bar x$ = 99.74.

The standard deviation is s = 58.

The sample size n = 584.

Using the t-test formula yields the following results:

$t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}}$

Consequently, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025

We calculate $t_{\alpha /2}$ = -1.65

Substituting values into the t-test formula gives t = -0.108338, producing a p-value of p = 0.4569, which exceeds α, hence we accept the null hypothesis, indicating that there is adequate statistical evidence supporting the average location of Wade Tract = 100.