# Confidence

To find the average age of a penny in circulation, 884 pennies were collected by 13 students of St. Francis High School. The sample mean and standard deviation was:

n = 884
mean = 1986.359 (that is 12.641 years old is the average age)
standard deviation = 9.247 years

Omitting the 1944 penny (an outlier.. the next oldest was 1959):
n = 883
mean = 86.407
standard deviation = 9.142

But it took great effort to tabulate this many pennies. Could we get an estimate by checking fewer pennies? How about one penny? Five? Ten? One Hundred? Let's find out.

Randomly select a penny from the sample of 884 pennies, and type the score in the box, recording the mean and standard deviation. Do this for the the follwing sample sizes:
meanS.D.2*S.D.mean - (2*S.D.)mean + (2*S.D.)Hit?
One penny
Three pennies
Five pennies
Ten pennies
15 pennies
20 pennies

## Data:

 n=
Is there much differece? Would it help to grab a sample of larger than 20 pennies? Test your ideas why.

## Standardize

Compare your sample means with the known means. One way to standardize this is to subtract the mean from your score, and divided by the known standard deviation. This is the Z - score. Since we know that 95% of the time the sample mean will be 2 standard deviations away from the mean, double your sample S.D. and then add and subtract it to your sample mean. This gives you the 95% Z interval. Did the actual mean fall within your interval? Next part...