Question

Collect fifty pennies and record the year that each was minted. Once you have found the year each coin was minted determine the age of each coin in year Each student should have his or her own sample. Fill in the table below with the data you selected for your random sample:

Obs#	Age	Obs#	Age	Obs#	Age	Obs#	Age	Obs#	Age
1	1	11	3	21	37	31	1	41	1
2	45	12	1	22	23	32	1	42	2
3	27	13	7	23	1	33	38	43	1
4	23	14	37	24	25	34	35	44	44
5	1	15	1	25	26	35	22	45	1
6	1	16	25	26	19	36	20	46	5
7	15	17	3	27	2	37	5	47	25
8	1	18	12	28	29	38	29	48	4
9	17	19	7	29	1	39	1	49	6
10	4	20	1	30	2	40	40	50	2

Draw a histogram for the age of the coins (in years) for your sample. (You may use technology and insert the histogram below or you may print this document and draw it by hand. Be sure that, either way, it is neat and clearly labeled.)

Is the t-distribution valid in this problem? Explain why or why not – including any necessary calculations. (Remember there are three conditions you should be checking.)

Did you have any outliers? If so, describe them

Calculate the mean and standard deviation for your sample.

Sample Statistic	Symbol	Calculated Value
Sample Mean
Sample Standard Deviation

Use your sample to compute a 98% confidence interval for the mean age of pennies in circulation. Show all necessary calculations including the standard error and how you found the critical value. Write a sentence to describe the meaning of the confidence interval in the context of this problem.

We Know Coinz Ltd., a national numismatic organization, believes that the average age of pennies in circulation is greater (older) than that of the average age of quarters in circulation. They have estimated the average age of quarters in circulation to be approximately 16.75 years. Use the sample data you have collected to carry out the appropriate hypothesis test to answer the question: Is the average age of pennies in circulation greater than the estimated average age of quarters?

Write the null and alternative hypotheses you would use to investigate the answer to that question. Write them in symbolic notation AND write each hypothesis statement in a sentence.

Carry out the hypothesis test. Including: (1) make a sketch of the sampling distribution with the axis labeled to show the mean and standard error, (2) mark the sample mean and shade the appropriate area and (3) show calculations of the test statistic and the pvalue. Use a significance level of 0.05.

State your decision about the hypothesis test and then state your conclusion carefully in the context of this problem.

Answer 1