Purchase Solution

Bayes Theorem - Decision Analysis - Type I & Type II errors

Not what you're looking for?

Ask Custom Question

See the attached file.

Need step-by-step instructions on how to solve the following example problems:

Decision Analysis

The quality control manager in a chip manufacturing plant has to select one of two available quality control methods. The estimated error rates for the methods are presented below: (see attachment)

Type I error probability is defined as the conditional probability of rejecting a good lot. Type II error probability is defined as the conditional probability of accepting a poor quality lot.

Historical data suggests that four percent of the lots produced in the plant are of poor quality.

a. Based on the information specified above, what is the conditional probability that:
(i) A lot rejected by using method A is actually good?
(ii) A lot accepted by using method A is actually bad?
(iii) A lot rejected by using method B is actually good?
(iv) A lot accepted by using method B is actually bad?

b. The organization incurs a cost of $4,000 when it rejects a good lot. It is further estimated that the cost of accepting a poor lot is $ 10,000 (due to liabilities). If the objective is to minimize the expected cost of errors, which quality control method should the manager adopt? Why?

c. For the current manufacturing process, the a-priori probability that a lot is poor is 0.04. Under what ranges of this probability should the manager to prefer method A? Assume that all other parameters remain as specified in (a) and (b).

d. Under what ranges for the cost of accepting a poor lot should the manager to prefer method A? Assume that all other parameters remain as specified in (a) and (b).

Attachments
Purchase this Solution
Solution Summary

The solution assists with computing Type I and Type II errors, Conditional Probability formulas and Bayes' theorem.

Solution Preview

See attached.

1. We have:
P(Type 1 error) = P(Reject Ho/ Ho is True)
P(Type 2 error) = P( Accept Ho/ Ho False)
Now, from what is given, we conclude:
For method A
P(Reject Ho/Ho True) = .04
P(Accept Ho/Ho is false)= .02
For method B
P(Reject Ho/Ho True) = .02
P(Accept Ho/Ho is false)= .02
We will make the following notations:
B: Event lot is bad quality (Ho is ...

Solution provided by:
Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
Recent Feedback
  • "Thank you "
  • "Thank You Chris this draft really helped me understand correlation."
  • "Thanks for the prompt return. Going into the last meeting tonight before submission. "
  • "Thank you for your promptness and great work. This will serve as a great guideline to assist with the completion of our project."
  • "Thanks for the product. It is an excellent guideline for the group. "
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Hypothesis Testing And Central Limit Theorem

    540791 The solution gives detailed steps on determining type I and type II errors in a specific hypothesis testing and using confidence interval method to make the conclusion of the same test.

  • Use of Bayes' theorem in health care administration

    Bayes' theorem allows you to consider the actual probability of an event given the measured test probabilities, unlike traditional statistics. (the probability of error) I.e. -"Correct for measurement errors.

  • Test for one population mean

    Write the decision rule using the p-value approach. c. Write the Type I and Type II Errors d. What is the probability of making a Type I error Given the following null and alternative hypotheses.

  • Type I and type II Errors, Statistical Significance

    308592 Type I and Type II Errors: Statistical Significance Question 1: What is a type I and type II errors in hypothesis testing? What would be examples of each?

  • Type I Error

    The probability of a Type I error (α) is called the significance level and is set by the experimenter. There is a tradeoff between Type I and Type II errors.

  • Decision Under Uncertainty - Bayes' Theorem

    524087 Decision Under Uncertainty - Bayes' Theorem Need help with the following: Research statistical data in a business context that requires a decision. Use probability concepts found in Bayes' Theorem to formulate a decision.

  • Are Type I or Type II Errors More Concerning?

    We must take the means and find standard errors, which we can then apply tests to. Only in those tests do the type I and type II errors show up. In statistical analysis, do we care about type I or II errors more?

  • Jury and Type I and Type II Errors

    179711 Jury and Type I and Type II Errors Using null hypothesis and alternative hypothesis if juries must make a decision about the guilt or innocence of a defendant: Suppose you are on a jury of a murder trial.

  • Statistics - Type I and Type II errors - Examples

    271763 Statistics - Type I and Type II errors - Examples Describe the five steps of hypothesis testing. Compare Type I and Type II errors and give specific examples for each. Which error should be minimized the most and first?

View More Related Solutions