Your simple test may or may not tell you anything. Often the base metal under silver plate is the same color as silver, so when the silver wears away you can't really tell. Sterling silver is an alloy commonly used for such things, along with silver plate. It would be highly unlikely your items are made of pure silver. Sterling is a composition of 92.5% silver, 7.5% copper. Scandinavian countries used different alloys of silver and copper, some as low as 70% silver. The marks on your pieces should tell you what they are made of. Look for a number like 925, which would be sterling, 900, which would be "coin" silver, Also look for hallmarks, such as a lion. Tell us what you see marked on the bottom of your pieces and we may be able to tell you what you bought.
If you are interested in a non-destructive test for silver, there is a solution that will react blood red when applied to silver, a mixture of distilled water, nitric acid and potassium dichromate. Nitric acid alone will also react, leaving a cream colored surface on the item being tested if it is silver, but a green reaction if you test a scratch through a plated item. None of this is difficult, but if you haven't seen the tests done before you may not understand what you are seeing when doing the tests. If you can provide more information I may be able to tell you more. .