Question

In an article in the journal Health and Place, Hui and Bell found that among 2428 boys ages 7 to 12 years, 461 were overweight or obese. On the basis of this study, can we conclude that more than 15 percent of the boys ages 7 to 12 in the sampled population are obese or overweight? Let alpha=0.05. Conduct a hypothesis test by hand.

Answer 1

Given

n = sample size = 2428

x = over weight = 461

p = 15% = 0.15

Claim : more than 15% of the boys ages 7 to 12 in the sampled population are obese or overweigh

Hypothesis :

Test Statistics :

Z = 5.51

Using Z table for 5.51 we get probability 1 ( 5.51 is 3.49 so we assume probability 1. But 1 is left tailed probability we have right tailed so we subtract 1 from 1 or you use excel command =1-normsdist(5.51))

P( Z > 5.51) = 1-1 = 0.00

P value = 0.0000

P value < 0.05 so we reject null hypothesis.

Conclusion :

We have sufficient evidence to conclude that more than 15% of the boys ages 7 to 12 in the sampled population are obese or overweigh .