Refer to Example 5.8 on 0 vegetarians in a sample of n = 20 and Exercises 5.77 and 5.77.

(a) At the Inference for a Proportion applet at www.artofstat.com/webapps.html, enter 0 successes for n = 20. Explain why the reported standard error values differ when you click on Confidence Interval and when you click on Significance Test and enter a null hypothesis value such as 0.50 for π.

(b) To test H0: π = 0.50, show what happens if you find the z test statistic using the se =



πˆ (1 − πˆ )/n formula for confidence intervals. Explain why se0 =



π0(1 − π0)/n is more appropriate for tests.