Question

Bark beetles are tiny insects with hard, cylindrical bodies that reproduce under the bark of trees. While bark beetles are native to U.S. forests and play important ecological roles, they can cause extensive tree mortality and negative economic and social impacts. Researchers at Los Alamos National Laboratory are interested in the behavior of Bark Beetles living in the Santa Fe National Forest. In particular, they are interested in the average size of these beetles (body length measured in mm). They assume that the distribution of body length for these beetles can be modeled with a Normal distribution with mean μ and standard deviation σ. After spending several weeks in the field, they have measured and recorded the body length of 263 of these beetles. The average body length of these 263 beetles is 6.14mm with a calculated standard deviation of 1.89mm.

1. What is the population of interest?

2. What is the sample size?

3. What is the sample?

4. What parameters are mentioned in this problem? Explain what the parameters mean in terms of the problem.

5. What is the sample data?

6. What are the estimators mentioned in this problem? For each estimator, explain which parameter it is supposed to estimate.

7. What are the estimates for the parameters in this problem?

Answer 1

Answer 1.

The Population of interest is the one which we want to study and make inferences for using some representative samples.

Here,The Population of Interest is the Population of Bark Beetles native to U.S. forests.

Answer 2.

Sample Size is 263. That is, we will be studying 263 beetles to make inferences about the average body lengths of bark beetles are native to U.S. forests.

Answer 3.

Sample is a representative subset of thePopulation used to make inferences about the population.

Here, Sample is the set of 263 Bark Beetles living in the Santa Fe National Forest.

Answer 4.

Here we are given the distribution of body length for these beetles can be modeled with a Normal distribution with mean μ and standard deviation σ.

The Parameters are:

The Mean Body Lengths μ which gives the average size or average body lengths of beetles measured in mm.

The Standard Deviation σ which tells us how far or how close the actual body length or sizes of beetles lie to the average size μ i.e. how much the actual sizes disperse from the mean sizes.

Answer 5.

The Sample Data is the Actual Body Length or Sizes of 263 Bark Beetles in mm obtained from Santa Fe National Forest.

Answer 6.

The Estimators mentioned in this problem are:

a. Sample Mean,

b. Sample Standard Deviation,

Now, the Sample Mean, will be used to estimate the population mean μ & Sample Standard Deviation, will be used to estimate Population Standard Deviation

Answer 7.

The Estimates of the Paramters are: