Question

In a random sample of 65 professional actors, it was found that 43 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,

n = 65

x = 43

(a)

= x / n = 43 / 65 = 0.662

1 - = 1 - 0.662 = 0.338

(b)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.662 * 0.338) / 65)

= 0.115

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.662 - 0.115 < p < 0.662 + 0.115

0.547 < p < 0.777

Lower limit = 0.55

Upper limit = 0.78