Let ? denote the true average tread life of a certain type of tire. Consider testing H0: ? = 30,000 versus Ha: ? > 30,000 based on a sample of size n = 16 from a normal population distribution with ? = 1500. A test with ? = 0.01 requires z? = z0.01 = 2.33. The probability of making a type II error when ? = 31,000 is ? = Φ 2.33 + 30,000 − 31,000 1500/ 16 = Φ (rounded to two decimal places) = 0.3669

Let ? denote the true average tread life of a certain type of tire. Consider testing H0: ? = 30,000 versus Ha: ? > 30,000 based on a sample of size n = 16 from a normal population distribution with ? = 1500. A test with ? = 0.01 requires z? = z0.01 = 2.33. The probability of making a type II error when ? = 31,000 is ? = Φ 2.33 + 30,000 − 31,000 1500/ 16 = Φ (rounded to two decimal places) = 0.3669

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

Let ? denote the true average tread life of a certain type of tire. Consider testing H₀: ? = 30,000 versus H_a: ? > 30,000 based on a sample of size n = 16 from a normal population distribution with ? = 1500. A test with ? = 0.01 requires z_? = z_0.01 = 2.33. The probability of making a type II error when ? = 31,000 is

= Φ

2.33 +

30,000 − 31,000

1500/

= Φ

(rounded to two decimal places)

= 0.3669

Since z_0.1 = 1.28, the requirement that the level 0.01 test also have ?(31,000) = 0.1 necessitates

n =

1500(2.33 + 1.28)

30,000 − 31,000

	2

= (−5.42)² =

(rounded to two decimal places).

The sample size must be an integer, so n = (rounded up to the next whole number) tires should be used.

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