MATH HELP!! - Statistics

Question

Test the claim that the proportion of people who own dogs is less than 31%. A random sample of 1000 people found that 28.8% owned dogs. Do the sample data provide convincing evidence to support the claim? Test the relevant hypothesis using a 5% level of significance. Give an answer to at least 4 decimal places.

Answer 1

use a binomial, asjust 2categories,own dogs or not

x=1000(p)= 280

xbar=310

var=310(.79)=244.9

sd=sqr244.9= about 15.6493

alpha=.05

CI=310+/-15.6493(1.96), 1.96= about 2

= about (310-31.2986, 310+41.2986)

280 is in the 95% CI

fail to reject Ho: mean=31% dog owners

but what about one dog with 2 owners?