The amount of wear on a shaft (0.0001 in) after a fixed mileage was determined for each of n = 8 internal combustion engines with lead-copper bearings and obtained = 3.72 and s = 1.25. (a) Assuming that the shaft wear distribution is normal with mean μ, use the test at the 0.05 level to test H0: μ = 3.50 against H1: μ > 3.50. (b) With σ = 1.25, what is the probability of type II error (β) of the test if the alternative were μ = 4.00?

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The amount of wear on a shaft (0.0001 in) after a fixed mileage was determined for each of n = 8 internal combustion engines with lead-copper bearings and obtained = 3.72 and s = 1.25.

(a) Assuming that the shaft wear distribution is normal with mean μ, use the test at the 0.05 level to test H0: μ = 3.50 against H1: μ > 3.50.


(b) With σ = 1.25, what is the probability of type II error (β) of the test if the alternative were μ = 4.00?


Note:
The exercise in the image is in Spanish, to make the exercise more understandable.

4.- Se determinó la cantidad de desgaste en una flecha (0.0001 pulg) después de un kilometraje fijo
para cada uno de n = 8 motores de combustión interna con cojinetes de plomo al cobre y se obtuvo
x = 3.72 y s = 1.25.
a) Suponiendo que la distribución del desgaste de la flecha es normal con media µ, use la prueba
a un nivel de 0.05 para probar Ho: µ = 3.50 contra H1: µ > 3.50.
b) Con o = 1.25, ¿cuál es la probabilidad de error de tipo II (B) de la prueba si la alternativa fuera
H = 4.00?
Transcribed Image Text:4.- Se determinó la cantidad de desgaste en una flecha (0.0001 pulg) después de un kilometraje fijo para cada uno de n = 8 motores de combustión interna con cojinetes de plomo al cobre y se obtuvo x = 3.72 y s = 1.25. a) Suponiendo que la distribución del desgaste de la flecha es normal con media µ, use la prueba a un nivel de 0.05 para probar Ho: µ = 3.50 contra H1: µ > 3.50. b) Con o = 1.25, ¿cuál es la probabilidad de error de tipo II (B) de la prueba si la alternativa fuera H = 4.00?
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