It is difficult to conduct sample surveys on sensitive issues because many people will not answer questions if the answers might embarrass them. Randomized response is an effective way to guarantee anonymity while collecting information on topics such as student cheating or sexual behavior. Here is the idea. To ask a sample of students whether they have plagiarized a term paper while in college, have each student toss a coin in private. If the coin lands heads and they have not plagiarized, they are to answer "No." Otherwise they are to give "Yes" as their answer. Only the student knows whether the answer reflects the truth or just the coin toss, but the researchers can use a proper random sample with follow-up for nonresponse and other good sampling practices. Suppose that in fact the probability is 0.4 that a randomly chosen student has plagiarized a paper. Draw a tree diagram in which the first stage is tossing the coin and the second is the truth about plagiarism. The outcome at the end of each branch is the answer given to the randomized-response question.

Question
Asked Jul 27, 2019
309 views

It is difficult to conduct sample surveys on sensitive issues because many people will not answer questions if the answers might embarrass them. Randomized response is an effective way to guarantee anonymity while collecting information on topics such as student cheating or sexual behavior. Here is the idea. To ask a sample of students whether they have plagiarized a term paper while in college, have each student toss a coin in private. If the coin lands heads and they have not plagiarized, they are to answer "No." Otherwise they are to give "Yes" as their answer. Only the student knows whether the answer reflects the truth or just the coin toss, but the researchers can use a proper random sample with follow-up for nonresponse and other good sampling practices. Suppose that in fact the probability is 0.4 that a randomly chosen student has plagiarized a paper. Draw a tree diagram in which the first stage is tossing the coin and the second is the truth about plagiarism. The outcome at the end of each branch is the answer given to the randomized-response question.

check_circle

Expert Answer

Step 1

Tree diagram:

It is a graphical representation of all the possible outcomes of an event. Each branch in a tree diagram represents a possible outcome. There are two branches. The probability of each branch is written on the branch. The outcome is written at the end of the branch.

Step 2

It is given that if the coin shows head and they have not plagiarized they are to answer ‘No’ and otherwise they are to give ‘Yes’. The probability that a randomly chosen student has plagiarized a paper is 0.4.

Here, the first branch represents the outcome o...

Yes
0.4
Head
0.6
0.5
No
Coin
0.5
0.5
Tail
Yes
help_outline

Image Transcriptionclose

Yes 0.4 Head 0.6 0.5 No Coin 0.5 0.5 Tail Yes

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the...

A: According to the given question, Jane has stored three albums on her iPod.The first album consists o...

question_answer

Q: Number 15 A B C D

A: Note:Thank you for the question. However, your question has more than 3 parts. We are solving first ...

question_answer

Q: you gave me this answer in last question, (copied below) but I see why I wasn't finding the correct ...

A: Note:Thank you for letting us know your doubt. We shall try our best to help you understand clearly ...

question_answer

Q: Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of mu equals 8.0 ...

A: Part (a): Level of significance:In the given information, it is said that “Alpha = 0.01”. Now, “Alph...

question_answer

Q: What is the “third factor” problem concerning correlational studies as it relates to inferring causa...

A: The correlation between any two variables is the linear relationship between those variables, but it...

question_answer

Q: Find the critical value tc for the confidence level c=0.98 and sample size n=21

A:  The critical value tc for 98% confidence level with sample size 21:The confidence level is 98%. Tha...

question_answer

Q: A group of students decide to participate in a national strength test. Assume a normal distribution ...

A: Given mean number of students participated in national strength test = 580Standard deviation = 72.5T...

question_answer

Q: Professor Jennings claims that only 35% of the students at Flora College work while attending school...

A: (a) Level of significance:It is given that to test whether more than 35% of the students have jobs, ...

question_answer

Q: An advertising executive wants to determine if a new billboard placed in a city caused sales of thei...

A: Given that we need to test to determine if a new billboard played in a city caused sales of their pr...