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 5,320 permanent dwellings on an entire reservation showed that 1,662 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

Solution :

Given that,

n = 5320

x = 1662

Point estimate = sample proportion = = x / n = 1662/5320=0.3124

1 -   = 1-0.3124= 0.6876

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* (((0.3124*0.6876) /5320 )

E = 0.016

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.3124 - 0.016 < p < 0.3124+0.016

lower limit 0.296

upper limit 0.328