A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be ¯x < 14.9. (a) Find the probability of committing a type I error when H0 is true. (b) Evaluate β for the alternatives μ = 14.8 and μ = 14.9 kilograms.

A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be ¯x < 14.9. (a) Find the probability of committing a type I error when H0 is true. (b) Evaluate β for the alternatives μ = 14.8 and μ = 14.9 kilograms.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Question

A manufacturer has developed a new fishing
line, which the company claims has a mean breaking
strength of 15 kilograms with a standard deviation of
0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms, a
random sample of 50 lines will be tested. The critical
region is defined to be ¯x < 14.9.
(a) Find the probability of committing a type I error
when H0 is true.
(b) Evaluate β for the alternatives μ = 14.8 and μ =
14.9 kilograms.

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