Young men tend to think they need more muscle to be attractive. One study presen

Question

Young men tend to think they need more muscle to be attractive. One study presented 200 young men in a country with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter (kg/m^2) of fat-free body mass. Typical young men have about 20 kg/m^2. Each subject chose two images, one that represented his own level of body muscle and one that he thought represented "what women prefer." The mean gap between self-image and "what women prefer" was 2.05 kg/m^2. Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.1 kg/m^2. Give a 90% confidence interval for the mean amount of muscle young men think they should add to be attractive to women. (They are wrong: women actually prefer a level close to that of typical men. Round your answers to three decimal places.) to kg/m^2 You may need to use the appropriate Appendix Table to answer this question.

Explanation / Answer

sample size =n=200, mean gap=2.05 and standard deviation=sd=2.1

(1-alpha)*100% confidence interval for gap =sample mean gap ± z(alpha/2)*sd/sqrt(n)

90% confidence interval =2.05±z(0.1/2)*2.1/sqrt(200)=2.05±1.6449*2.1/sqrt(200)=2.05±0.2443=(1.8057, 2.2943)

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