Health issues due to being overweight affect all age groups. of children and adolescents 6-11 years of age,18.8% are found to be overweight. A school district randomly sampled 130 in this age group and found that 20 were considered overweight. at Alpha =.05 is this less than the national proportion?

Question

I have worked this out but got a different answer so I need to see if I am doing this correctly.
This is what I have X=263, N=500, Alpha =.05 H0 p=.47 h1 p not = .47this is the claim.

Answer 1

p hat = x/n = 263/500 = .526

z = (.526-.47)/√.526*.474/500)
z = 0.056/√.249324/500)
z = 2.50779
P-value = 0.0121

Answer 2

Think you messed up z=(.526-.47)/sqrt.526*.474/500)it should be Z=(.526-.47)/(.47)(.53)/sqrt 500 = am I right Sir

Answer 3

.526-.470 = 0.056