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The 2010 National Youth Physical Activity and Nutrition Study interviewed an SRS

ID: 3156953 • Letter: T

Question

The 2010 National Youth Physical Activity and Nutrition Study interviewed an SRS of 9701 high school students about a number of health issues. According to the Centers for Disease Control and Prevention (CDC), 18.4% of adolescents were obese in 2010. Let’s assume that the proportion of obesity among all American high school students is p=0.184.

(a) What are the mean and standard deviation of the proportion of the sample who are obese?

(b) Are the conditions for inference satisfied? Explain why or why not?

Explanation / Answer

a)

As given, the mean of proportions is

u(p^) = p = 0.184 [ANSWER]

and the standard deviation is

s(p^) = sqrt(p(1-p)/n) = sqrt(0.184*(1-0.184)/9701) = 0.003934103 [ANSWER]

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b)

Yes, as the sample size (9701) is less than 5% of all adolescents. Also, the sample size is large enough as np and n(1-p) are both greater than 10 for n = 9701, p = 0.184.