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 67 professional actors, it was found that 37 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p̂ = q̂ =

b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Find the maximal margin of error. (Round your answer to two decimal places.)

E =  

Report the bounds from the 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit=

upper limit=

Answer 1

Solution :

Given that,

n = 67

x = 37

= x / n = 37 / 67 = 0.5522

q̂ = 1 - = 1 - 0.5522 = 0.4478

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * (((0.5522 * 0.4478) / 67)

Margin of error   = 0.12

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.5522 - 0.12 < p < 0.5522 + 0.12

0.43 < p < 0.67

(0.43,0.67)

The 95% confidence interval for p is 0.43 to 0.67.

The bonds from 95% confidence interval for p

Lower limit = 0.43

Upper limit = 0.67