Question

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

In a random sample of 530 judges, it was found that 279 were introverts.

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

lower limit
upper limit

Answer 1

Solution :

Given that,

n = 530

x = 279

Point estimate = sample proportion = = x / n = 279/530=0.5264

1 -   = 1- 0.5264=0.4736

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* (((0.5264*0.4736) /530 )

E = 0.0559=0.06

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5264-0.06 < p < 0.5264+0.06

0.47< p < 0.59