A scientific paper reported the following summary information on fracture toughnesses (MPa) of n = 169 ceramic bars fired in a particular kiln: = 89.10, s = 3.73.a) Calculate a confidence interval (bilateral) for the average true fracture toughness using a 95% confidence level. Could it be said that the average true fracture toughness was accurately estimated?b) Assume that the investigators believed a priori that the population standard deviation was approximately 4 MPa. Based on this assumption, how large a sample would have to be to estimate μ to within 0.5 MPa with 95% confidence for each side?Note:The exercise in the image is in Spanish, to make the exercise more understandable. 1.- Un artículo científico reportó la siguiente información resumida sobre resistencias a la fractura(MPa) de n = 169 barras de cerámica horneadas en un horno particular: i = 89.10, s = 3.73.a) Calcule un intervalo de confianza (bilateral) para la resistencia a la fractura promedioverdadera utilizando un nivel de confianza de 95%. ¿Se podría decir que la resistencia a lafractura promedio verdadera fue estimada con precisión?b) Suponga que los investigadores creyeron a priori que la desviación estándar de lapoblación era aproximadamente de 4 MPa. Basado en esta suposición, ¿qué tan grandetendría que ser una muestra para estimar u hasta dentro de 0.5 MPa con 95% deconfianza para cada lado?

Given,sample size (n) = 169sample mean (x̄) =89.10sample standard deviation (s) = 3.73a)…

A scientific paper reported the following summary information on fracture toughnesses (MPa) of n = 169 ceramic bars fired in a particular kiln: = 89.10, s = 3.73. a) Calculate a confidence interval (bilateral) for the average true fracture toughness using a 95% confidence level. Could it be said that the average true fracture toughness was accurately estimated? b) Assume that the investigators believed a priori that the population standard deviation was approximately 4 MPa. Based on this assumption, how large a sample would have to be to estimate μ to within 0.5 MPa with 95% confidence for each side? Note: The exercise in the image is in Spanish, to make the exercise more understandable.

A scientific paper reported the following summary information on fracture toughnesses (MPa) of n = 169 ceramic bars fired in a particular kiln: = 89.10, s = 3.73. a) Calculate a confidence interval (bilateral) for the average true fracture toughness using a 95% confidence level. Could it be said that the average true fracture toughness was accurately estimated? b) Assume that the investigators believed a priori that the population standard deviation was approximately 4 MPa. Based on this assumption, how large a sample would have to be to estimate μ to within 0.5 MPa with 95% confidence for each side? Note: The exercise in the image is in Spanish, to make the exercise more understandable.

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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