Chapter 4.1, Problem 15E

(a)

To determine

To explain why it would not be practical for scientists to obtain an SRS in this setting.

Explanation of Solution

Given that:

Total pine trees $=5000$

Population size $=5000$

Sample pine trees $=200$

This implies sample size $=200$

Now, in case of $5000$ pine trees which is spread around highway.

Now, we have to select $200$ trees from that but practically we select more trees near by highway than trees which are from highway or vice versa. But practically we do not select $200$ trees such that every trees has equal chance of selection. Thus, probability of selecting every treesis not same. Therefore, according to definition of SRS, it would not be practical for scientist to obtain an SRS in this setting.

(b)

To determine

To explain why is this sampling method biased.

Explanation of Solution

A possible alternative would be to use first $200$ pine trees along the highway as you enter the park.

In this case, we only select first $200$ pine trees. So, it is possible that first $200$ trees are not so much infected than remaining tree or it is also possible that the infection pine beetles is more near the highway than other trees.

So, if we only study about first $200$ trees than there is bias for result and we do not get perfect result for study. Therefore, this idea is good.

(c)

To determine

To find out can scientist conclude that exactly $35\%$ of all the pine trees on the west side of the park are infected and explain why or why not.

Answer to Problem 15E

Yes.

Explanation of Solution

Systematic sampling: in this sampling starting from a random point on a sampling frame, every nth element in the frame is selected at equal interval.

In this study, total trees $=5000$

And sample pine trees $=200$

Therefore, interval for selection,

  $\frac{5000}{200}=25$

It means we select every $25$ th tree from starting at first three and end at $5000$ th tree. So, we get $200$ trees at interval of $25$ trees from $5000$ tree. In this sampling entire population cover. So, study of this sampling give accurate result for infection in trees and proportion of infection in trees.