Many of you have hit on some of the keey points of a confidence interval. Essentially its a statisitical tool that we use to make estimates about certain population parameters. Though its true that we can look at the confidence interval of various population parameters, for our purpose in this class we will be looking at the confidence interval for the mean of a population. What this means is we will be using sample information to make a determination about the mean of a population.

You have mentioned that the confidence interval gives us a range and not a single number. That is true. The cofidence interval will not solve an individual value as the estimate for the population mean. Instead the confidence interval reveals the range of numbers that we feel the true population mean falls between. So when make a conclusion using the confidence interval test our statements will always say that we are (%) so cofident that the mean of the population falls between x and y.

The problem will always deteremine the level of confidence we are testing at.

Let's look at an example,

Let's say a fleet manager takes 100 tires and tests their mean useful life to be 45,000 miles with a standard deviation that is known to be 5,000.

Test the mean useful life of all tires at 95% level of confidence.

Testing for a 95% confidence interval means we are allowing 5% for the possibility of error so we call this our Alpha level = .05

Now the formula we need to know to solve our confidence interval is as follows:

Sample mean - Allowable error Sample mean + Allowable error

Using Excel to assist, goto Formula > More Functions > Statistical > CONFIDENCE

Alpha = .05

Standard Deviation = 5,000

(Sample) Size = 100

We get a result back of 979.982 which I will call 980. I now take my allowable error that Excel calculated and put it in my confidence interval formula:

45,000 - 980 45,000 + 980

44,020 459,980

Therefore we are 95% confident that the mean useful life of all truck tires is between 44,020 and 45,980 miles.

Develop a 90% confidence interval for the same tires.