Suppose a researcher obtains a grant to study the health and nutrition (or lack thereof) at...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose a researcher obtains a grant to study the health and nutrition (or lack thereof) at a university with a large undergraduate population. To begin the study, a random sample of n = 100 undergrads is drawn and their current weights are taken and recorded, with a recorded average weight of y 145 pounds. Let's assume that the weights of the undergrad population follow a normal distribution with unknown mean and known standard deviation 20 pounds. Further suppose that, before taking the observed data, a prior distribution for was specified to be normal with mean 175 and a conservative standard deviation of 35 pounds. = (a) Write down the posterior distribution for (you may use results given in the lecture slides). Then, simulate 10,000 draws from the posterior distribution and make a histogram of the draws. (4 points) (b) Using your simulated draws from part (a), estimate using the posterior median and give an equal-tailed 95% posterior interval for 0. (2 points) (c) Generally, calculating HPD intervals/regions can be complicated. For this example, what can we say about the HPD interval in relation to the equal-tailed interval given above? (1 point) Suppose a researcher obtains a grant to study the health and nutrition (or lack thereof) at a university with a large undergraduate population. To begin the study, a random sample of n = 100 undergrads is drawn and their current weights are taken and recorded, with a recorded average weight of y 145 pounds. Let's assume that the weights of the undergrad population follow a normal distribution with unknown mean and known standard deviation 20 pounds. Further suppose that, before taking the observed data, a prior distribution for was specified to be normal with mean 175 and a conservative standard deviation of 35 pounds. = (a) Write down the posterior distribution for (you may use results given in the lecture slides). Then, simulate 10,000 draws from the posterior distribution and make a histogram of the draws. (4 points) (b) Using your simulated draws from part (a), estimate using the posterior median and give an equal-tailed 95% posterior interval for 0. (2 points) (c) Generally, calculating HPD intervals/regions can be complicated. For this example, what can we say about the HPD interval in relation to the equal-tailed interval given above? (1 point)
Expert Answer:
Related Book For
Business Statistics A First Course
ISBN: 9780321979018
7th Edition
Authors: David M. Levine, Kathryn A. Szabat, David F. Stephan
Posted Date:
Students also viewed these mathematics questions
-
A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (in inches) of each trees main stem was measured. The resulting observations are as follows: a. Compute a point...
-
A normal population has a known mean 50 and unknown variance. (a) A random sample of n = 16 is selected from this population, and the sample results are x = 52 and s = 8. How unusual are these...
-
Using techniques from Section 8.2, we can find a confidence interval for μd. Consider a random sample of n matched data pairs A, B. Let d = B - A be a random variable representing the...
-
Utility is a type of function that occurs in eco-nomics. When a consumer receives a units of a product, a certain amount of pleasure, or utility U, is gained. The following represents a typical...
-
Outline the steps in preparing an operating budget.
-
Water is pumped between two large open reservoirs through \(1.5 \mathrm{~km}\) of smooth pipe. The water surfaces in the two reservoirs are at the same elevation. When the pump adds \(20...
-
What is the purpose of filing a lis pendens?
-
Metros computer system generated the following trial balance on December 31, 2011. The companys manager knows that the trial balance is wrong because it does not show any balance for Goods in Process...
-
Find the amount of energy used by a freezer to make 1.5kg of water at 20 degrees Celsius into ice at -12 degrees Celsius
-
The following unadjusted trial balance is for Power Demolition Company as of the end of its April 30, 2013, fiscal year. The April 30, 2012, credit balance of the owners capital account was $46,900,...
-
Last year Attic charged $3,164,000 Depreciation on the Income Statement of Andrews. If early this year Attic purchased a new depreciable asset, the effect on Andrews's financial statements would be...
-
I am having the same issue with this LAB: Number pattern Here is my code: def print_num_pattern(num1,num2): if (num1 == 0 or num1 < 0): print(num1, end = ' ') return print(num1, end = ' ')...
-
Explain the basics of activity-based costing. You have to take one example and explain that fully . Explain the benefits and limitations of activity-based costing. Not less than eight. Explain cost...
-
48. The period (time for a complete oscillation) of a simple pendulum depends on the pendulum's length L and the acceleration of gravity g. The dimensions of L are L, and the dimensions of gare L/T....
-
I need help I have this code that I can get to print out however, I need it to print out in reverse here is my code def readFile(filename): dict = {} with open(filename, 'r') as infile: lines =...
-
Research Chipotle In a document what are chipotle internal strengths and internal weaknesses? What are some market opportunities and market threats? What is chipotle strategy? If you are introducing...
-
What amount was invested 35 years ago at 7% compounded semiannually if the value of the investment has now grown to $1,000,000? Round to the nearest dollar.
-
The swap spread is the difference between the swap rate and the equivalent-maturity Treasury bond yield. Explain why a widening swap spread may be a signal of deteriorating economic conditions. Plot...
-
What is the relationship between the price of crude oil and the price you pay at the pump for gasoline? The file Oil & Gasoline contains the price ($) for a barrel of crude oil (Cushing, Oklahoma,...
-
Your task as a member of the International Strategic Management Team in your company is to investigate the potential for entry into a foreign market. As part of your initial investigation, you must...
-
What are the differences between a priori probability, empirical probability, and subjective probability?
-
Solve Prob. 8-48 using Castigliano's theorem. Data From Problem 8.48 = ABC 6.5(103) mm IBC 100(10) mm+ AAB = 18(10) mm IAR 400(10) mm+ DA = 3 m B -50 kN 1 m
-
Solve Prob. 8-40 using Castigliano's theorem. Data From Problem 8.40 2 k/ft 8 ft 8 ft B
-
Solve Prob. 8-53 using Castigliano's theorem. Data From Problem 8.53 8 k 10 ft. 8 ft D A B
Study smarter with the SolutionInn App