Question

Independent random samples were taken of male and female members of University Entrepreneurship Club. These members were considering starting a business. Of 500 members, 200 actually started a business venture.
a. Estimate the value of the population proportion. (Round your answers to 3 decimal places.)

b. Develop a 99% confidence interval for the population proportion.

Answer 1

Solution:

Let 'n' be the total number of members and 'x' be the number of members who are actually started a business venture.

Given: n=500, x=200 and Confidence level=99%

a)The value of population proportion, =x/n=200/500=0.4

b)Calculation of confidence interval

For 99% confidence level, z-value=2.58

Formula to find confidence interval is given by

z-value*

0.42.580.4(1-0.4)/500

0.4(2.58*0.022)

[(0.4-0.057),(0.4+0.057)]

[0.343,0.457]

Therefore the 99% confidence interval for the population proportion lies between 0.343 and 0.457.

Please give thumbs up if you are happy with the answer.Thank you.