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 534 judges, it was found that 288 were introverts.

(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)

(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 = 534

x = 288

Point estimate = sample proportion = = x / n = 288/534=0.5393

1 - = 1-0.5393=0.4607

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 (((0.5393*0.4607) /534 )

E = 0.06

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5393- 0.06< p < 0.5393+0.06

0.4793< p < 0.5993

The 99% confidence interval for the population proportion p is : lower limit=0.48,upper limit=0.60