The Age of a Coin

Math 171-01 Project:

THE AGE OF A COIN

“I have neither nor received help on this assignment, nor am I aware of any infraction of the honor code.”

Walter J. Coleman

Kevin A. Napier

Brandon D’sa

The coins used in this study consists of change collected over time by Kevin Napier. However, since “over time” refers to the past year according to Napier, the coins are likely to be mostly recently created. In that way, most of the ages will be similar which could create a skew in the data.
The population for this study would be all minted quarters and pennies, the individuals are each of the quarters and pennies. *******************Variables *******************
Graphs

Histogram of penny ages:

Histogram of quarter ages:

Tables:

Age of pennies

Pennies
Sample mean: / 22.64
Sample standard deviation: / 15.73992713
Minimum: / 0
Quartile 1: / 9
Median: / 23.5
Quartile 3: / 34
Maximum: / 56

Interquartile range (IQR): 25

Q[3] + 1.5*IQR = 71.5

Q[1] - 1.5*IQR = -28.5

No outliers.

Age of quarters

Quarters
Sample mean: / 17.84
Sample standard deviation: / 12.23137485
Minimum: / 0
Quartile 1: / 9
Median: / 15
Quartile 3: / 23
Maximum: / 48

Interquartile range (IQR): 14

Q[3] + 1.5*IQR = 44

Q[1] – 1.5*IQR = -12

46 and 48 are outliers.

The distribution of quarter and penny ages are both slightly skewed to the right, possibly because most coins are still used from the past. Likewise, the graphs were for the most part, very similar. For example, the sample mean for the age of quarters is only five less than the sample mean for the age of pennies. Likewise, the sample standard deviation of quarters is only three less than the sample standard deviation of quarters. However, the difference in the sample means is not noticeable.
I believe that the distribution of all coins in circulation is similar to the distribution of our samples because there are fifty pennies and fifty quarters in the samples. Furthermore, Napier is a relatively generic American, and his collection of coins likely resembles the distribution of all coins.
The distribution is not an
Confidence Interval

-Pennies

1)The mean age of pennies

2)T-interval; SRS: not given (use caution); sigma is unknown; no strong skew and no outliers; sample size >30

3)(18.167 & 27.113)

4)We are 95% confident that the mean age of pennies is between 18.167 and 27.113 years

-Quarters

1)The mean age of quarters

2)T-interval; SRS: not given (use caution); sigma is unknown; no strong skew and no outliers; sample size > 30

3)(13.468 & 19.782) *Note that 2 outliers were taken out of the data

4)We are 95% confident that the mean age of pennies is between 13.468 and 19.782 years

Margin of error for quarters = 4.473
Margin of error for pennies = 3.157
The sample size necessary to estimate the proportion of pennies in circulation that are older than 20 years to within 2% with 98% confidence is n=((InvNorm(.99,0,1) / .02)^2) (27/50) (1-(27/50)) = 3360.786451… round up so 3361
Using InvNorm(.98,sample mean, sample standard deviation) would work to find the rare pennies that are equal to or less than 2% of the population, because it would cover the younger 98% of the sample, and therefore would indicate the age in which the oldest 2% of pennies would be.
(X^2)GOFtest

1.)p[1] = proportion of pennies that are younger than 10 years old

p[2] = proportion of pennies that are between 10 and 20 years old

p[3] = proportion of pennies that are older than 20 years old

Expected: p[1] = .25, p[2] = .5, p[3] = .25

Observed: p[1] = .26, p [2] = .2, p[3] = .54

2.)qualitative, all expected counts are > 5

3.)H[0]: p[1] = .25, p[2] = .5, p[3] = .25

H[a]: At least one of the proportions are not as specified

4.)Test Statistic: 25.84

5.)P-value: .0000024485856

6.)There is significant evidence at the 5% significance level (p = 0.000002449) that at least one of the proportions is not as specified in the expected proportions of pennies that are a certain age.

T-Test:

1.)Parameter = proportion of quarters that were produced in the past 30 years

2.)No SRS; use caution, no outliers, population standard deviation unknown, no strong skew, sample size is above 30

3.)H[0]: p = .62

H[a]: p != .62

4.)Test statistic: t=10.19753627

5.)P=0.00000000000017

6.)There is significant evidence that the proportion of quarters that were produced in the past 30 years is .62.

7.)************************************

19 proportion of pennies= .38 and the proportion of quarters= .1667. Therefore, proportion of coins minted before 1984 is not equal.

Age of Pennies:

Age of Quarters: