Question

Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood. A botanist studying the region suspects that the proportion might be greater than 0.60. The botanist obtained a random sample of trees from the region and conducted a test of H0:p=0.6 versus Ha:p>0.6. The p-value of the test was 0.015. Which of the following is a correct interpretation of the p-value?1. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6. 2. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as small as or smaller than the one obtained by the botanist. 3. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist. 4. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist. 5. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

Answer 1

Answer:

1. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

Step-by-step explanation:

Hello!

The historical information indicates that 60% of the forest trees are classified as softwood.

A botanist thinks that the proportion might be greater than 60%, so he tested his belief obtaining:

H₀: p = 0.60

H₁: p > 0.60

p-value: 0.015

You need to interpret this p-value. Little reminder:

The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis. It represents the % of size n samples from a population with proportion p=p₀, which will produce a measure that provides evidence as (or stronger) than the current sample that p is not equal to p₀.

The correct answer is:

1. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

I hope this helps!