Answered: Suppose that a group of researchers is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, σ, is 1.5 lb.

To show that the supplement is effective, they plan to use a one-sample z‑test of H0:μ=0 lb against H1:μ>0 lb, where μ is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01, the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb.

What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places.

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