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 532 judges, it was found that 294 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 = 532

x = 294

Point estimate = sample proportion = = x / n = 294/532 = 0.5526

1 - = 1-0.5526= 0.4474

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z_{0.005 = 2.576}

Z/2 = 2.576

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

= 2.576 * ((0.5526*(0.4474) / 532)

= 0.056

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.5526 -0.056 < p < 0.5526+0.056

( 0.50 , 0.61 )

Lower limit = 0.50

Upper limit = 0.61