Question

Wildlife biologists inspect 132 deer taken by hunters and find 28 of them carrying ticks that test positive for Lyme disease.

1) Create a​ 90% confidence interval for the percentage of deer that may carry such ticks.

​2) If the scientists want to cut the margin of error in​ half, how many deer must they​ inspect? ​

3) What concerns do you have about this​ sample?

A. Since deer ticks are parasites and can easily be spread from one deer to​ another, the ticks may not be distributed evenly throughout the deer population.

B. Since females and young deer are usually not​ hunted, this sample may not be representative of all deer.

C. Since females and young deer are usually not​ hunted, this sample may not be representative of all deer.​ Also, since deer ticks are parasites and can easily be spread from one deer to​ another, the ticks may not be distributed evenly throughout the deer population.

D. There are no concerns about this study.

Answer 1

1) = 28/132 = 0.212

At 90% confidence level, the critical value is z_0.05 = 1.645

The 90% confidence interval is

2) The number of deer must be inspected to cut the margin of error in half = 132 * 4 = 528

3) Option - C) Since females and young deer are usually not hunted, this sample may not be representative of all deer. Also, since deer ticks are parasites and can easily be spread from one deer to another, the ticks may not be distributed evenly throughout the deer population.