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 70 professional actors, it was found that 37 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 = 37 / 70 = 0.5286

1 - = 1 - 0.5286 = 0.4714

b) Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.5286 * 0.4714) / 70)

= 0.12

A 95% confidence interval for population proportion p is ,

± E

= 0.5286   ± 0.12

= ( 0.41, 0.65 )

lower limit = 0.41

upper limit = 0.65