Question

The production employees at a garment factory have been surveyed several times to determine the proportion of employees who are opposed to a union. The estimates of this proportion ranged from 60% to 80%. The management agrees that they want a 90% confidence interval estimate with a halfwidth of 2%. What sample size should they use?

Answer 1

Solution :

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.60 + 0.80) / 2

Point estimate = = 0.70

1 - = 1 - 0.70 = 0.30

margin of error = E = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

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

= (1.645 / 0.02)2 * 0.70 *0.30

= 1420.66

sample size = n = 1421