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 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 = 0.6615

1 - = 1 - 0.6615 = 0.3385

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 = 1.960

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

= 1.960 * (((0.66 * 0.44 ) / 65)

= 0.13

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

- E < P < + E

0.66 - 0.13 < p < 0.66 + 0.13

0.53 < p < 0.79

lower limit = 0.53

upper limit = 0.79