Question

1. A. An union representing the Bottle Blowers of America (BBA) is considering a proposal to merge with the Teamsters Union. According to BBA bylaws, at least three-fourths of the union membership must approve any merger. A random sample of 2,000 current BBA members reveals 1,600 plan to vote for the merger proposal. Develop a 95% confidence interval for the population proportion. Show point estimate, standard error and margin of error and finally your confidence interval.

Basing your decision on this sample proportion, can you conclude that the necessary         proportion of BBA members favor the merger? Why?                                                       

      B. The estimate of the population proportion is to be within plus or minus 0.10, with a 99% confidence coefficient level. The best estimate of the population proportion is given as 45%. How large a sample is required under these specifications?                                          

Answer 1

A) = 1600/2000 = 0.8

SE = sqrt((1 - )/n)

     = sqrt(0.8 * 0.2/2000)

     = 0.0089

At 95% confidence interval the critical value is z_0.025 = 1.96

Margin of error = z_0.025 * SE

                      = 1.96 * 0.0089

                      = 0.0174

The 95% confidence interval for population proportion is

+/- E

= 0.8 +/- 0.0174

= 0.7826, 0.8174

B) At 99% confidence interval the critical value is z_0.005 = 2.575

Margin of error = 0.1

or, z_0.005 * sqrt(P(1 - P)/n) = 0.1

or, 2.575 * sqrt(0.45 * (1 - 0.45)/n) = 0.1

or, n = (2.575 * sqrt(0.45 * 0.55)/0.1)^2

or, n = 165