The small-sample method is a good approximation to Wilsons method for all confidence levels commonly used in practice, but is best when z2 is close

The small-sample method is a good approximation to Wilson’s method for all confidence levels commonly used in practice, but is best when zα∕2 is close to 2. Refer to Exercise 41.

a. Use Wilson’s method to construct a 90% confidence interval, a 95% confidence interval, and a 99% confidence interval for the proportion of tenth graders who plan to attend college.

b. Use the small-sample method to construct a 90% confidence interval, a 95% confidence interval, and a 99% confidence interval for the proportion of tenth graders who plan to attend college.

c. For which level is the small-sample method the closest to Wilson’s method? Explain why this is the case.

Wilson’s interval: The small-sample method for constructing a confidence interval is a simple approximation of a more complicated interval known as Wilson’s interval. Let p̂ = x∕n.
Wilson’s confidence interval for p is given by

Exercise 41

In a certain high school, 9 out of 15 tenth graders said they planned to go to college after graduating. Construct a 95% confidence interval for the proportion of tenth graders.

2 2 Za/2 + p(1 - p) Za/2 2n 2a/2 + n 4n2 1+ Za/2 2 n