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 510 judges, it was found that 275 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,

(a)

Point estimate = sample proportion = = x / n = 275 / 510 = 0.5392

1 - = 1 - 0.5392 = 0.4608

Z_/2 = 2.576

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

= 2.576 * (((0.5392 * 0.4608) / 510)

= 0.06

(b)

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.5392 - 0.06 < p < 0.5392 + 0.06

0.48 < p < 0.60

lower limit : 0.48

upper limit : 0.60