/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 15 Dead trees On the west side of R... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 15 (page 237)

Dead trees On the west side of Rocky Mountain National Park, many mature pine trees are dying due to infestation by pine beetles. Scientists would like to use sampling to estimate the proportion of all pine trees in this area that have been infested.

a. Explain why it wouldn鈥檛 be practical for scientists to obtain an SRS in this setting.

b. A possible alternative would be to use every pine tree along the park鈥檚 main road as a sample. Why is this sampling method biased?

c. Suppose that a more complicated random sampling plan is carried out, and that 35% of the pine trees in the sample are infested by the pine beetle. Can scientists conclude that exactly 35% of all the pine trees on the west side of the park are infested? Why or why not?

Short Answer

Expert verified

a. Scientists would not be able to obtain an SRS in this situation, according to the definition of SRS.

b. It's likely that the first 200trees aren't as infected as the rest of the trees, or that the infection pine beetles are more concentrated near the highway than in other trees.

c. Starting from a random point on a sample frame, every nth element in the frame is selected at equal intervals in systematic sampling, selection interval is25

Step by step solution

01

Part (a) Step 1 : Given Information

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

02

Part (a) Step 2 ; Simplification

Given that:

Total pine trees =5000

Population size = 5000

Sample pine trees = 200

This implies sample size = 200

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

Now we have to choose 200 trees from that, but in practice, we choose trees that are closer to the highway than trees that are farther away, or vice versa. However, we do not select trees in such a way that each tree has an equal probability of being selected. As a result, the likelihood of selecting each tree is not the same. As a result, scientists would not be able to obtain an SRS in this situation, according to the definition of SRS.

03

Part (b) Step 1 : Given Information

We have to explain why is this sampling method biased.

04

Part (b) Step 2 ; Simplification

The first 200pine trees along the highway as you enter the park might be used as an alternative.

Only the top 200pine trees are chosen in this scenario. As a result, it's likely that the first 200trees aren't as infected as the rest of the trees, or that the infection pine beetles are more concentrated near the highway than in other trees.

As a result, if we just investigate the first 200trees, the results will be biased, and the study will not yield a perfect result.

05

Part (c) Step 1 : Given Information

We have 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.

06

Part (c) Step 2 ; Simplification

Starting from a random point on a sample frame, every nth element in the frame is selected at equal intervals in systematic sampling.

The total number of trees in this study is = 5000

Also, have a look at some pine trees =200

As a result, the selection interval,

5000200=25

It indicates that we choose every 25th tree starting with the first three and ending with the 500th tree. So, from 5000trees, we get 200trees at intervals of 25trees. This sampling covers the entire population. As a result, analysis of this sampling yields reliable results for tree infection and infection proportion.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the experiment of the preceding exercise, the subjects were randomly assigned to the

different treatments. What is the most important reason for this random assignment?

a. Random assignment eliminates the effects of other variables such as stress and body

weight.

b. Random assignment is a good way to create groups of subjects that are roughly

equivalent at the beginning of the experiment.

c. Random assignment makes it possible to make a conclusion about all men.

d. Random assignment reduces the amount of variation in blood pressure.

e. Random assignment prevents the placebo effect from ruining the results of the study.

Initial public offerings (1.3) The business magazine Forbes reports that 4567companies sold their first stock to the public between 1990and 2000. The mean change in the stock price of these companies since the first stock was issued was +111%. The median change was -31%. Explain how this difference could happen.

Got deodorant? A group of students wants to perform an experiment to determine

whether Brand Aor Brand Bdeodorant lasts longer. One group member suggests the

following design: Recruit 40student volunteers鈥�20male and20female. Separate by

gender, because male and female bodies might respond differently to deodorant. Give all

the males Brand Adeodorant and all the females Brand B. Have the principal judge how

well the deodorant is still working at the end of the school day on a 0to 10scale. Then

compare ratings for the two treatments.

a. Identify any flaws you see in the proposed design for this experiment.

b. Describe how you would design the experiment. Explain how your design addresses

each of the problems you identified in part (a).

Sampling the forestTo gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10%of the plots.

a. Explain how you would use a random number generator to choose an SRS of 141plots. Your description should be clear enough for a classmate to carry out your plan.

b. Use your method from part (a) to choose the first 3plots.

Cocoa and blood flow A study of blood flow involved 27healthy people aged 18to 72. Each subject consumed a cocoa beverage containing 900milligrams of flavonols daily for 5days. Using a finger cuff, blood flow was measured on the first and fifth days of the study. After 5 days, researchers measured what they called 鈥渟ignificant improvement鈥� in blood flow and the function of the cells that line the blood vessels. What flaw in the design of this experiment makes it impossible to say if the cocoa really caused the improved blood flow? Explain your answer.

See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.