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 60 professional actors, it was found that 36 were extroverts.

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

(b) Find a 95% 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 = 36 / 60 = 0.6000

1 - = 1 - 0.6000 = 0.4000

Z_/2 = Z0.025 = 1.96

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

= 1.96 * (((0.6000 * 0.4000) / 60)

= 0.1240

b) A 95% confidence interval for population proportion p is ,

- E < p < + E

0.6000 - 0.1240 < p < 0.6000 + 0.1240

0.48 < p < 0.72

lower limit = 0.48

upper limit = 0.72