Men and muscle Ask young men to estimate their own degree of body muscle by choosing

Chapter 8, Problem 67

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QUESTION:

Ask young men to estimate their own degree of body muscle by choosing from a set of 100 photos. Then ask them to choose what they believe women prefer. The researchers know the actual degree of muscle, measured as kilograms per square meter of fat-free mass, for each of the photos. They can therefore measure the difference between what a subject thinks women prefer and the subject's own self-image. Call this difference the "muscle gap". Here are summary statistics for the muscle gap from a random sample of 200 American and European young men: \(\bar{x}=2.35\) and \(\mathrm{s}_{\mathrm{x}}=2.5\)

(a) Calculate and interpret a 95% confidence interval for the mean size of the muscle gap for the population of American and European young men.

(b) A graph of the sample data is strongly skewed to the right. Explain why this information does not invalidate the interval you calculated in part (a).

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QUESTION:

Ask young men to estimate their own degree of body muscle by choosing from a set of 100 photos. Then ask them to choose what they believe women prefer. The researchers know the actual degree of muscle, measured as kilograms per square meter of fat-free mass, for each of the photos. They can therefore measure the difference between what a subject thinks women prefer and the subject's own self-image. Call this difference the "muscle gap". Here are summary statistics for the muscle gap from a random sample of 200 American and European young men: \(\bar{x}=2.35\) and \(\mathrm{s}_{\mathrm{x}}=2.5\)

(a) Calculate and interpret a 95% confidence interval for the mean size of the muscle gap for the population of American and European young men.

(b) A graph of the sample data is strongly skewed to the right. Explain why this information does not invalidate the interval you calculated in part (a).

ANSWER:

Step 1 of 5

A confidence interval (CI) is a statistical concept used to estimate the range within which a population parameter, such as the mean or proportion, is likely to fall. It provides a range of values, along with a level of confidence, that is believed to contain the true parameter.

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