Refer to Exercise 41.

a. Which of the three confidence intervals is the narrowest?

b. Does the small-sample method provide a good approximation to Wilson’s interval in this case?

c. Explain why the traditional interval is the widest of the three.

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.

Transcribed Image Text:

Za/2 + 2n 2 2a/2 1+ p(1 - p) + Za/22 4n2 Za/2 n 2 n