Question

A random sample of 5200 permanent dwellings on an entire reservation showed that 1571 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)
lower limit
upper limit

Answer 1

Given that

A random sample of 5200 permanent dwellings on an entire reservation showed that 1571 were traditional hogans.

Sample proportion p =
`(1571)/(5200) =0.3021`

p follows a normal distribution with mean = 0.3021 and variance

=
`(pq)/(n) =(0.3021(0.3677))/(5200) =0.00002136`

std dev of p=0.00462

For 99% confidence level we use Z critical value 2.58

Margin of errror = 2.58 (std error) =0.0119

Confidence interval lower bound = 0.3021-0.0119 =0.2902

Upper bound = 0.3021+0.0119 =0.3140

Answer 2

p^ = 1571/5200 = 0.3021

99% C I = 0.3021 + or - 2.58sqrt((0.3021(1 - 0.3021))/5200) = 0.3021 + or - 0.0064 = 0.296 to 0.309
lower limit = 0.296
upper limit = 0.309