HW3

1. (4 points)

From Lohr Exercise 2.10 Which of the following SRS designs will give the most precision (smallest variance) for estimating the population mean? Assume that each population has the same value of the population variance $S^2$. Please report the variance of the estimator for each scenario as a function of $S^2$ and then state which is the smallest.

1. An SRS of size 400 from a population of size 4000
2. An SRS of size 30 from a population of size 300
3. An SRS of size 3000 from a population of size 300,000,000

2.

Using the bird data set from Lab 2, a SRS sample of size 15 grid squares has been drawn for you.

birds <- read.csv('http://math.montana.edu/ahoegh/teaching/stat446/birdsurvey.csv', header = T)
set.seed(09252019)
sample_values <- sample(birds$bird.counts, size = 15)

a. (4 points)

Compute an estimate of the total number of birds across the entire region composed of 200 grid squares.

b. (4 points)

Using the FPC compute the variance of the estimator for the population total.

c. (4 points)

Construct a 95\% confidence interval for the population total.

d. (4 points)

Discuss the similarities and differences for calculating uncertainty in our point estimates between this approach and the repeated sampling procedure from Lab 3.