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Problem 11.57eb: There exists a constant C such that C * s? has a well-known probability distribution. Report the appropriate degrees of freedom for that distribution

Problem 11.57eb: There exists a constant C such that C * s? has a well-known probability distribution. Report the appropriate degrees of freedom for that distribution

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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QUESTION 8 Problem 11.57eb: There exists a constant C such that C * s? has a well-known probability distribution. Report the appropriate degrees of freedom for that distribution. Hint: L-23: p 14
Transcribed Image Text:QUESTION 8 Problem 11.57eb: There exists a constant C such that C * s? has a well-known probability distribution. Report the appropriate degrees of freedom for that distribution. Hint: L-23: p 14
Ag. 11.57 A researcher conducts an experiment to examine the relationship between the weight gain of chickens whose diets had been supplemented by different amounts of the amino acid lysine and the amount of lysine ingested. Since the percentage of lysine is known and we can monitor the amount of feed consumed, we can determine the amount of lysine eaten. A random sample of 12 2-weck-old chickens was selected for the study. Each was caged separately and was allowed to cat at will from feed composed of a base supplemented with lysine. The sample data summarizing weight gains and amounts of lysine eaten over the test period are given here. (In the data, y represents weight gain in grams, and x represents the amount of lysine ingested in grams.) a. From the scatterplot of the data, does a lincar model seem appropriate? b. Compute the estimated linear regression model ŷ = B, + B,x. Weight Gain, Lysine Ingested, y (in grams) Weight Gain, Lysine Ingested, y (in grams) Chick x (in grams) Chick x (in grams) 1 14.7 09 7 17.2 .11 2 17.8 .14 18.7 .19 3 19.6 .18 20.2 23 18.4 .15 10 16.0 .13 5 20.5 .16 11 17.8 .17 21.1 23 12 19.4 21 11.58 Refer to Exercise 11.57. a. Estimate o. b. Compute the standard error of B,. c. Conduct a statistical test of the rescarch hypothesis that for this diet preparation and length of study, there is a direct (positive) linear relationship between weight gain and amount of lysine eaten. 11.59 Refer to Exercise 11.57. a. For this exercise, would it make sense to give any physical interpretation to B,? (Hint: The lysine was mixed in the feed.) b. Consider an alternative model relating weight gain to amount of lysine ingested: y = Bix +e Distinguish between this model and the model y = Bo + Bix + e. 11.60 a. Refer to part (b) of Exercise 11.59. Obtain 8, for the model y = B,x + e, where Exy b. Which of the two models, y Bo+ Bix + c or y Bx + e, appears to give a better fit to the sample data? (Hint: Examine the two prediction equations on a graph of the sample observations.) 比
Transcribed Image Text:Ag. 11.57 A researcher conducts an experiment to examine the relationship between the weight gain of chickens whose diets had been supplemented by different amounts of the amino acid lysine and the amount of lysine ingested. Since the percentage of lysine is known and we can monitor the amount of feed consumed, we can determine the amount of lysine eaten. A random sample of 12 2-weck-old chickens was selected for the study. Each was caged separately and was allowed to cat at will from feed composed of a base supplemented with lysine. The sample data summarizing weight gains and amounts of lysine eaten over the test period are given here. (In the data, y represents weight gain in grams, and x represents the amount of lysine ingested in grams.) a. From the scatterplot of the data, does a lincar model seem appropriate? b. Compute the estimated linear regression model ŷ = B, + B,x. Weight Gain, Lysine Ingested, y (in grams) Weight Gain, Lysine Ingested, y (in grams) Chick x (in grams) Chick x (in grams) 1 14.7 09 7 17.2 .11 2 17.8 .14 18.7 .19 3 19.6 .18 20.2 23 18.4 .15 10 16.0 .13 5 20.5 .16 11 17.8 .17 21.1 23 12 19.4 21 11.58 Refer to Exercise 11.57. a. Estimate o. b. Compute the standard error of B,. c. Conduct a statistical test of the rescarch hypothesis that for this diet preparation and length of study, there is a direct (positive) linear relationship between weight gain and amount of lysine eaten. 11.59 Refer to Exercise 11.57. a. For this exercise, would it make sense to give any physical interpretation to B,? (Hint: The lysine was mixed in the feed.) b. Consider an alternative model relating weight gain to amount of lysine ingested: y = Bix +e Distinguish between this model and the model y = Bo + Bix + e. 11.60 a. Refer to part (b) of Exercise 11.59. Obtain 8, for the model y = B,x + e, where Exy b. Which of the two models, y Bo+ Bix + c or y Bx + e, appears to give a better fit to the sample data? (Hint: Examine the two prediction equations on a graph of the sample observations.) 比
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