Question Solved1 Answer Funding agencies, and others who sponsor research, do not want to see their money wasted. They require that the studies they fund have sufficient statistical power. (a) What does it mean to say a given study has 80% power? (b) Imagine two proposed study designs for research on a similar topic. In study A, the researchers anticipate that the slope will be approximately 3 with a standard error of 1. In study B the researchers expect a slope of 5 with standard error 3. In both studies the researchers propose to test the null hypothesis that B1 = 0. Which study has the greater chance of rejecting the null? Explain your answer. (c) To increase the power of a study, without increasing the sample size, how could the research designs be modified? Give two specific suggestions and explain why the changes would improve the power.

JWCDEI The Asker · Probability and Statistics

Transcribed Image Text: Funding agencies, and others who sponsor research, do not want to see their money wasted. They require that the studies they fund have sufficient statistical power. (a) What does it mean to say a given study has 80% power? (b) Imagine two proposed study designs for research on a similar topic. In study A, the researchers anticipate that the slope will be approximately 3 with a standard error of 1. In study B the researchers expect a slope of 5 with standard error 3. In both studies the researchers propose to test the null hypothesis that B1 = 0. Which study has the greater chance of rejecting the null? Explain your answer. (c) To increase the power of a study, without increasing the sample size, how could the research designs be modified? Give two specific suggestions and explain why the changes would improve the power.
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Transcribed Image Text: Funding agencies, and others who sponsor research, do not want to see their money wasted. They require that the studies they fund have sufficient statistical power. (a) What does it mean to say a given study has 80% power? (b) Imagine two proposed study designs for research on a similar topic. In study A, the researchers anticipate that the slope will be approximately 3 with a standard error of 1. In study B the researchers expect a slope of 5 with standard error 3. In both studies the researchers propose to test the null hypothesis that B1 = 0. Which study has the greater chance of rejecting the null? Explain your answer. (c) To increase the power of a study, without increasing the sample size, how could the research designs be modified? Give two specific suggestions and explain why the changes would improve the power.
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(a)Power of a test is the probability of rejecting the null hypothesis when alternative is true. Thus, here 80% power means the probability of rejecting the null hypothesis when alternative is true is 0.80The power of a test indicates the strength of the test in detecting the effect if there is one. So, there are 80% chances of detecting the effect when there is one.(b){:[H_(0):beta_(1)=0","quadH_(a):beta_(1)!=0],[" Test statstic "=t_(cal)=( hat(beta)_(1))/(se( hat(beta)_(1)))]:}In first case:" Test statstic "=t_(cal)=(3)/(1)=3In second case:{:[" Test statstic "=t=(5)/(3)=1.6667],[P-" value "=P(|t| > t_("cal "))],[P(|t| > 3) < P(|t| > 1.6667)]:}The lesser is the p-value, the higher is the chances of rejecting the null hypothesisTherefore, probability of rejecting the null hypothesis will be greater in first case than in second case.(c)The power of ... See the full answer