10.103 A 2005 Harris Interactive for Korbel poll found that 63% of men and 55% of women think that it is okay for women to make marriage proposals to men. An 8% difference may or may not be statistically significant. What size sample is required to make this difference significant?

Source: USA Snapshot found on Internet, June 25, 2005

a. If the preceding sample statistics had resulted from a sample of 250 men and a sample of 250 women, would the difference be significant, using   0.05? Explain.

b. If the samples had each been of size 500, would the difference be significant, using

  0.05? Explain.

c. Determine the size sample that would have the difference of 0.08 corresponding to p  0.05.