Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5000 permanent dwellings on an entire reservation showed that 1669 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.)

= 0.3338

(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

lower limit
upper limit

Answer 1

Solution :

Given that,

n = 5000

x = 1669

a

Point estimate = sample proportion = = x / n = 1669/5000=0.334

1 -   = 1- 0.334 =0.666

b

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

  Margin of error = E = Z / 2    * (((( * (1 - )) / n)

= 2.576* (((0.334*0.666) /5000 )

E = 0.017

A 99% confidence interval is ,

- E < p < + E

0.334 - 0.017 < p < 0.334+0.017

0.317< p < 0.351

lower limit 0.317
upper limit 0.351