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 39 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 = 39 / 70 = 0.557

1 - = 0.43

Z_/2 = 1.96

(b)

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

= 1.96 * (((0.557 * 0.443) / 70)

= 0.12

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.557 - 0.12 < p < 0.557 + 0.12

0.44 < p < 0.67

Lower limit = 0.44

Upper limit = 0.67