Utilities must forecast the demand for energy use far into the future, because it takes decades to plan and build new power plants. Ron Bears, who worked for a Maritime utility company, had the job of predicting the proportion of households that would choose to use electricity to heat their homes. Although he was prepared to report a confidence interval for the true proportion, after seeing his preliminary report, his manager demanded a single number as his prediction.

Help Ron explain to his manager why a confidence interval for the desired proportion would be more useful for planning purposes. Explain how the precision of the interval and the confidence we can have in it are related to each other. Discuss the business consequences of an interval that is too narrow and the consequences of an interval with too low a confidence level.