Question

You plan to conduct a survey to find what proportion of the workforce has three or more jobs. You decide on the 99% confidence level and state that the estimated proportion must be within 4% of the population proportion. A pilot survey reveals that 6 out of 50 sampled hold three or more jobs. a. What is the point estimate for the proportion of students who hold three or more jobs? b. How many in the workforce should be interviewed to meet your requirements?

Answer 1

Solution :

Given that,

n = 50

x = 6

a)

Point estimate = sample proportion = = x / n = 0.12

1 - = 0.88

b)

margin of error = E = 0.04

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.04)2 * 0.12 * 0.88

= 437.96

sample size = 438