Pre1983 Post1982

Pre-1983	Post-1982
<1983 Pennies	?1983 Pennies
3.1582	2.5113
3.0406	2.4907
3.0762	2.5024
3.0398	2.5298
3.1043	2.4950
3.1274	2.5127
3.0775	2.4998
3.1038	2.4848
3.1086	2.4823
3.0586	2.5163
3.0603	2.5222
3.0502	2.5004
3.1028	2.5248
3.0522	2.5058
3.0546	2.4900
3.0185	2.5068
3.0712	2.5016
3.0717	2.4797
3.0546	2.5067
3.0817	2.5139
3.0704	2.4762
3.0797	2.5004
3.0713	2.5170
3.0631	2.4925
3.0866	2.4876
3.0763	2.4933
3.1299	2.4806
3.0846	2.4907
3.0917	2.5017
3.0877	2.4950
2.9593	2.4973
3.0966	2.5252
2.9800	2.4978
3.0934	2.5073
3.1340	2.4658
	2.4529
	2.5085

Here are the null and alternate hypotheses for your means Z-test: H0 : mu

Solution

1 Sample

Sample Size

35

Sample Mean

3.0748

Sample Standard Deviation

0.0391

2 Sample

Sample Size

37

Sample Mean

2.4991

Sample Standard Deviation

0.0165

Standard Error

0.0071

Difference in Sample Means

0.5757

Test Statistic

80.5950

Z=80.595

P=0.0000

Since calculated P=0.0000 < 0.05 level, here is significant difference between average weight of the two sets of pennies.

1 Sample
Sample Size	35
Sample Mean	3.0748
Sample Standard Deviation	0.0391
2 Sample
Sample Size	37
Sample Mean	2.4991
Sample Standard Deviation	0.0165
Standard Error	0.0071
Difference in Sample Means	0.5757
Test Statistic	80.5950