A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9(a) Find the probability of committing a type 1 error when H0H0 is true(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms. Example 2A manufacturer has developed a new fishing line, which he claims amean breaking strength of 15 kilograms with a standard deviationof 0.50 kilograms. To test the hypothesis that u = 15 kilogramsagainst the alternative that u < 15 kilograms, a random sample of 50lines will be tested. The critical region is defined to be a x<14.9.Assume o = 15 is correct.a) Find the probability of committing a type I error when H, is true.Evaluate B for the alternatives µ = 14.8 and u = 14.9 kilogramsb)

Given: μ=15, σ=0.5 The critical region is defined as X¯<14.9

tion of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9 (a) Find the probability of committing a type 1 error when H0H0 is true (b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms

tion of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9 (a) Find the probability of committing a type 1 error when H0H0 is true (b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms

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

A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9
(a) Find the probability of committing a type 1 error when H0H0 is true
(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms.