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 69 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,

n = 69

x = 39  

Point estimate = sample proportion = = x / n = 39 / 69 = 0.5652

1 - = 1 - 0.5652 = 0.4348

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 * (((0.5652 * 0.4348) /69 )

= 0.12

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.5652 - 0.12 < p < 0.5652 + 0.12

0.45 < p < 0.69

lower limit: 0.45

upper limit: 0.69

0.45 and