O Macmillan Learning Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter of body surface area (kg/m²). Typical young men have about 20 kg/m². 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 2.35 kg/m². Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5 kg/m². 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.) Give your answers to four decimal places. lower limit: upper limit: kg/m² kg/m²

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### Understanding Male Body Image Perceptions in North America and Europe

Many young men in North America and Europe, unlike those in Asia, tend to believe that increasing their muscle mass makes them more attractive. This assumption was explored in a study involving 200 young American men who were shown 100 images of men with varying muscle levels. The research involved measuring muscle mass in terms of kilograms per square meter of body surface area (kg/m²). It is found that the average young man has approximately 20 kg/m² of muscle.

Each participant in the study was asked to select two images: one that depicted their self-perceived muscle level and another illustrating how much muscle they thought women preferred. On average, the perceived "muscle gap" between self-images and perceived female preference was 2.35 kg/m².

#### Statistical Analysis

Suppose this "muscle gap" among all young men follows a normal distribution with a standard deviation of 2.5 kg/m². The task is to calculate a 90% confidence interval for the mean amount of muscle that young men think they need to gain to appeal to women. Notably, research indicates that women tend to prefer a muscle level much closer to the typical male's current state.

Fill in the following to find the confidence interval, rounded to four decimal places:

- **Lower Limit:** _______ kg/m²
- **Upper Limit:** _______ kg/m²

*Reference: Chi-Fu Jeffrey Yang, Peter Gray, and Harrison G. Pope, Jr. Male body image in Taiwan versus the West. American Journal of Psychiatry. 2005, 162, 263-269.*
Transcribed Image Text:### Understanding Male Body Image Perceptions in North America and Europe Many young men in North America and Europe, unlike those in Asia, tend to believe that increasing their muscle mass makes them more attractive. This assumption was explored in a study involving 200 young American men who were shown 100 images of men with varying muscle levels. The research involved measuring muscle mass in terms of kilograms per square meter of body surface area (kg/m²). It is found that the average young man has approximately 20 kg/m² of muscle. Each participant in the study was asked to select two images: one that depicted their self-perceived muscle level and another illustrating how much muscle they thought women preferred. On average, the perceived "muscle gap" between self-images and perceived female preference was 2.35 kg/m². #### Statistical Analysis Suppose this "muscle gap" among all young men follows a normal distribution with a standard deviation of 2.5 kg/m². The task is to calculate a 90% confidence interval for the mean amount of muscle that young men think they need to gain to appeal to women. Notably, research indicates that women tend to prefer a muscle level much closer to the typical male's current state. Fill in the following to find the confidence interval, rounded to four decimal places: - **Lower Limit:** _______ kg/m² - **Upper Limit:** _______ kg/m² *Reference: Chi-Fu Jeffrey Yang, Peter Gray, and Harrison G. Pope, Jr. Male body image in Taiwan versus the West. American Journal of Psychiatry. 2005, 162, 263-269.*
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