Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Statistics and Probability Expert

Detection and Estimation Theory

Project1

Hypothesis Testing Applied to Segregating A and B Students in a Detection and Estimation Course

An instructor wants to determine which of his students are A students and which are B students (this is a graduate course, so clearly all the students are either A or B students). The instructor gives a test to make this determination. This test contains 5 problems each worth 20 points. Both the A and B students will miss problems due to silly errors, incomplete knowledge (nobody is perfect), and time pressure (running out of time). The probability mass functions for the A and B students (single problem) are given below. Note that these probability mass functions are piecewise linear (this should help in getting the numbers.)

742_Hypothesis Testing_1.jpg

1. Given the total test score, generate a hypothesis test to minimize the probability of error supposing that 60% of the students are B students and 40% are students. For your hypothesis test, find out the probability that the instructor gives a student an A (student is segregated in the A group) if he deserves a B. Compute the probability that the instructor provides a student a B if he deserves an A.

2. You will require the density function for test scores for both A and B students to be capable to derive your hypothesis test. You must verify that you have the correct results through simulating the system and approximating the probabilities via statistics. You must also verify your probabilities of giving the student the wrong grade via your simulation. Note that the probability of a given score is approximated:  p (score) = # with score/total #

3. Some of you are probably saying: “What happens if we are all a students!!!” You are thinking that it is unfair to ascribe a priori that only 40% of the students are a students. We can avoid this a priori assumption by using the minimax test. Generate a minimax hypothesis test to segregate the students in A and B students. For the minimax hypothesis test, find out the probability that the instructor provides a student an A (student is segregated into the A group) if he deserves a B. find out the probability that the instructor gives a student a B if he deserves an A.

4. What occurs if the instructor gives harder problems? In this case, suppose the source probabilities in 1. Now, the probability mass functions for the A and B students (single problem) are given below. Note that these probability mass functions are again piecewise linear. Additional, the probability mass function for the A students is the same as the previous probability mass function for the B students. Create a hypothesis test for this case. For this test, find out the probability that the instructor gives a student an A (student is segregated in the A group) if he deserves a B. Compute the probability that the instructor gives a student a B if he deserves an A.

2006_Hypothesis Testing_2.jpg

5. What occurs if the instructor gives a shorter test? In this case, suppose that there are four problems, each problem is worth 25 points, and the source probabilities are as given in 1. Also suppose that due to less time pressure, students do better on these problems. The probability mass functions for the A and B students (single problem) are given below. Note that these probability mass functions are again piecewise linear. Create a hypothesis test for this case. For this test, find out the probability that the instructor gives a student an A (student is segregated into the A group) if he deserves a B. find out the probability that the instructor gives a student a B if he deserves an A.

659_Hypothesis Testing_3.jpg

Hand in:

1. An explanation of the hypothesis tests (must be four) with the derivation of relevant results. The probabilities of giving an A to a B student, and giving a B to an A student for each test must be included. Create a table of these probabilities for easy comparison.

2. Make sure to comprise enough equations and verbage (but it does not have to be long) so that I can follow what you did and verify that you did it correctly.

3. The information of your simulation program with enough documentation to be easily understood. Comprise the data indicating that your probabilities are correct. Note you only have to simulate the first case, but you can use your simulation to confirm the other cases if desired.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M91169
  • Price:- $80

Guranteed 48 Hours Delivery, In Price:- $80

Have any Question? 


Related Questions in Statistics and Probability

What is a critical value how is the critical value

"What is a critical value? How is the critical value determined? Are there differences between the standard normal table and the student t table when trying to determine the critical value? Explain."

Binomial stock option modelingsuppose you have the

Binomial Stock Option Modeling Suppose you have the opportunity to buy the following contract, a stock call option, on March 1. The contract allows you to buy 100 shares of XYZ stock at the end of either March, April, or ...

Candida has a revolving credit account at an annual

Candida has a revolving credit account at an annual percentage rate of 24%. Her previous monthly balance is $549.79. Find the new balance using the previous month's balance method if Candida's account showed the followin ...

1 what is the name of the statistic used in an anova2 if

1. What is the name of the statistic used in an ANOVA? 2. If the independent variable has no effect, the calculated value of F will be around 1.00. Why?

125 wordsexplain the history behind the black soldier of

125 words Explain the history behind the Black Soldier of the Civil War In this forum look beyond the book for information on specific units, soldiers and even the reasons for why Lincoln allowed the African American to ...

According to a recent poll 29 of adults in a certain area

According to a recent poll, 29% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major conce ...

1 gender was life better for women during the middle ages

1. GENDER Was life better for women during the Middle Ages than in past ages? What major events had an impact on their daily life? What role did magic play in the Middle Ages and how did it affect women? How were older w ...

Examine the history of american party politics from the

Examine the history of American party politics from the Great Depression through the 1990s. Trace the evolution of the major political parties, their policies, and their constituencies during this period.

Kindergarten children have heights that are approximately

Kindergarten children have heights that are approximately normally distributed about a mean of 38.8 inches and a standard deviation of 1.5 inches. If a random sample of 21 is taken, what is the probability that the sampl ...

Wat were the key political features of the roman republic

What were the key political features of the Roman Republic? How and why did this system of government collapse? Does our republic share any of the weaknesses of the Roman Republic?

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro