Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. 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. Find a 95% confidence interval for the difference between the proportions of unacceptable assemblies from the two teams.
b. Based on the confidence interval found in part a, is there sufficient evidence to conclude, at the 5% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies?
c. For which values of the difference between these two sample proportions could you conclude that a statistically significant difference exists at the 5% level?