For Exercises 55–58, software output for confidence intervals for are provided. Assume the conditions are met. For each, examine the indicated software output, and do the following:
55. Successful Weather Predictions. TI-83/84 results for a 95% confidence interval for , the population proportion of times the weather forecaster correctly predicted rain.
8.3.55
(a) (0.61018, 0.78982) (b) We are 95% confident that , the population proportion of times the weather forecaster correctly predicted rain, lies between 0.61018 and 0.78982. (c) 0.08982 (d) We can estimate the population proportion of times the weather forecaster correctly predicted rain to within 0.08982 with 95% confidence.