Let denote the true average tread life of a certain type of tire. Consider testi

Question

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

(.....) = (2.33 +( 30,000 31,000)/ (1500/(sqrt16)) = (.......) = 0.3669

Since z0.1 = 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 =......

The sample size must be an integer, so n = ....... tires should be used.

Explanation / Answer

Here (-5.42) 2 = 29.3764 ,when we are finding sample size we always round up the answer . So here our n= 30 (integer).

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