The values of outstanding bonds change whenever the going rate of interest changes. In
general, short-term interest rates are more volatile than long-term interest rates. Therefore,
short-term bond prices are more sensitive to interest rate changes than are long-term bond
prices. Is that statement true or false? Explain. (Hint: Make up a “reasonable” example
based on a 1-year and a 20-year bond to help answer the question.)

The answer is true!

You can find what the value of BONDS are
by checking at your nearest Stock Exchange.
You can always ring a broker for this information.

Princessmom, it's true that there's more volatility in short-term rates. But follow your question's "hint" advice to see why longer-dated cash flows are more sensitive to rate movements.

Use a very simple situation involving single cash flows: One maturing in 1 year, and the other occurring in 20 years. (These would correspond to zero-coupon bonds of 1-year and 20-year maturities, respectively.)

Price both of those instruments using any discount rate you like. Now tweak that discount rate and see which bond's price shows the bigger jump. Alternatively, you'd find that in order to make the short-term's price move by as much as the long-term bond's, you'll have to adjust the short-term rate a lot more than the amount of discount-rate adjustment you applied to the long.

While this effect is most pronounced in zero-coupon bonds, the same effect holds true for coupon-paying bonds, as well. The presence of the interim cash flows doesn't negate the effect, it only softens it very slightly. Again, do what the "hint" suggests and you'll see this easily.