MATH 534 Week 4 Discussion; Confidence Intervals in Business (Keller)

Confidenceintervalsrepresenttherangeofuncertaintyassociatedwiththeestimation of a statistic (mean, proportion, or standard deviation, etc.). There is always a risk ofsampling error associated with an estimate. Confidence intervals are useful forestablishing bounds for estimating, in particular, the mean or standard deviation, butalso regression coefficients, proportions, frequency rates, and differences betweenpopulations. Also, a 95% confidence interval indicates that for 19 out of 20 samplestakenfromthesamepopulation,theseintervalswillcontaintheparameterstudied,withamarginoferrorof5%. Letuselaboratewithanexample.Alightbulbmanufacturerwantstoestimatehowlonglight bulbs will work. It randomly samples 100 light bulbs and records the burn out timeto failure in a spreadsheet. Minitab allows calculating a 95% confidence interval of themean, with bounds of [] hours, for instance. The confidence intervalindicates that we can be 95% confident that the mean for the entire bulb population iswithin this range. However, although we know that the mean is likely to fall within therange,the95%confidenceintervaldoesnotpredictthat95%offutureobservationswillfallwithintherange. (Ogee,2021).