Question 6 (7 marks)

For each of the following parts, determine the lower and upper limits of the confidence interval for the parameter requested along with the best estimate of that parameter. No concluding statement is required

1. A random sample of size 100 from population 1 produced a proportion of successes of .45 while a sample of size 50 from population 2 produced a proportion of successes of .30. Calculate a 95% confidence interval for p₁ - p₂ and determine its best estimator.

2. A random sample of size 30 produced an average of 28.5 and a standard deviation of 4.2. Calculate a 90% confidence interval for and determine its best estimator. The value of the population variance was unknown.