Question

Independent random samples were taken of male and female members of University Entrepreneurship Club. These members...

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.

Homework Answers

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.

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