Introduction to Statistical Quality Control
7th Edition
ISBN: 9781118146811
Author: Montgomery, Douglas C.
Publisher: John Wiley & Sons Inc
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Chapter 3, Problem 11E
Construct and interpret a normal
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
Chapter 3 Solutions
Introduction to Statistical Quality Control
Ch. 3 - The content of liquid detergent bottles is being...Ch. 3 - The bore diameters of eight randomly selected...Ch. 3 - The service time in minutes from admit to...Ch. 3 - The Really Cool Clothing Company sells its...Ch. 3 - The nine measurements that follow are furnace...Ch. 3 - Consider the furnace temperature data in Exercise...Ch. 3 - Yield strengths of circular tubes with end caps...Ch. 3 - The time to failure in hours of an electronic...Ch. 3 - The data shown in Table 3E.2 are chemical process...Ch. 3 - An article in Quality Engineering (Vol. 4, 1992,...
Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct a normal probability plot of the failure...Ch. 3 - Construct a normal probability plot of the...Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Table 3E.4 contains 20 observations on cycles to...Ch. 3 - An important quality characteristic of water is...Ch. 3 - Consider the outpatient service times in Exercise...Ch. 3 - Consider the call handling limes in Exercise 3.4....Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Reconsider the yield data in Exercise 3.9....Ch. 3 - Consider the concentration of suspended solids...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Construct a box plot for the data in Exercise 3.1.Ch. 3 - Construct a box plot for the data in Exercise 3.2.Ch. 3 - Suppose that two fair dice are tossed and the...Ch. 3 - Find the mean and variance of the random variable...Ch. 3 - A mechatronic assembly is subjected to a final...Ch. 3 - The probability distribution of x is f(x) = kex, 0...Ch. 3 - The random variable x takes on the values 1, 2, or...Ch. 3 - The probability distribution of the discrete...Ch. 3 - A manufacturer of electronic calculators offers a...Ch. 3 - The net contents in ounces of canned soup is a...Ch. 3 - A production process operates with 1 %...Ch. 3 - Continuation of Exercise 3.35. Consider the...Ch. 3 - A random sample of 50 units is drawn from a...Ch. 3 - A sample of 100 units is selected from a...Ch. 3 - Suppose that 10% of the adult population has blood...Ch. 3 - Patients arriving at an outpatient clinic are...Ch. 3 - A stock brokerage has four computers that are used...Ch. 3 - A computer system uses passwords consisting of the...Ch. 3 - An electronic component for a medical X-ray unit...Ch. 3 - A lot of size N = 30 contains three nonconforming...Ch. 3 - A textbook has 500 pages on which typographical...Ch. 3 - Surface-finish defects in a small electric...Ch. 3 - Glass bottles are formed by pouring molten glass...Ch. 3 - The billing department of a major credit card...Ch. 3 - A production process operates in one of two...Ch. 3 - An inspector is looking for nonconforming welds in...Ch. 3 - The tensile strength of a metal part is normally...Ch. 3 - The output voltage of a power supply is normally...Ch. 3 - Continuation of Exercise 3.52. Reconsider the...Ch. 3 - If x is normally distributed with mean and...Ch. 3 - The life of an automotive battery is normally...Ch. 3 - A lightbulb has a normally distributed light...Ch. 3 - Derive the mean and variance of the binomial...Ch. 3 - Derive the mean and variance of the Poisson...Ch. 3 - Derive the mean and variance of the exponential...Ch. 3 - Derive the mean and variance of the geometric...
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