If n = 280 and ˆ p (p-hat) = 0.7, construct a 90% confidence interval.

Question

Give your answers to three decimals

If n = 280 and  (p-hat) = 0.7, construct a 90% confidence interval.

Answer 1

i will use p=p-hat

this is a binomial distribution that may be approximated as a normal distribution (because n>30),

where √(p(1-p)/n) is its standard deviation.

we looking in the table of normal distribution for a parameter t such that : p(z<t)=(1+α)/2 here we have α=90% so we looking for p(z<t)=0.95, in the table we get t=1.64

the confidence interval is given by [p-t*√(p(1-p)/n),p-t*√(p(1-p)/n)]

so [0.7-1.64*√(0.7(1-0.7)/280),0.7+1.64*√(0.7(1-0.7)/280)]

[0.66,0.74]

good luck