Two teams of workers assemble automobile engines at a manufacturing plant. Quality control personnel inspect a random sample of the teams assemblies and judge each assembly to be acceptable or unacceptable. A random sample of 127 assemblies from team 1 shows 12 unacceptable assemblies. A similar random sample of 98 assemblies from team 2 shows 5 unacceptable assemblies.

a. Construct a 90% confidence interval for the difference between the portions of unacceptable assemblies generated by the two teams.

b. Based on a review of the confidence interval found in part a, is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their portions of unacceptable assemblies. Conduct a hypothesis test to prove this theorem.

c. For which values of the differences between these two sample portions could you conclude that a statistically significant difference exists? (at alpha = .10 level)