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:

  1. Report the confidence interval in the form “(lower bound, upper bound).”
  2. Interpret the confidence interval.
  3. Calculate the margin of error for the confidence interval.
  4. Interpret the margin of error.

Question 8.232

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.

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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.