Is this sentence 'All else equal, a callable bond is more sensitive to interest rates than a non-callable bond.' correct? Why?

Yes, the sentence is correct. A callable bond is more sensitive to interest rate changes because the issuer of the bond has the option to call or redeem the bond at a specified price before its maturity date. This means that if interest rates fall, the issuer may choose to call the bond and issue new bonds at a lower interest rate, leaving the bondholder with lower coupon payments. Conversely, if interest rates rise, the issuer is less likely to call the bond, causing the bondholder to be stuck with a lower interest rate. This call feature adds an element of uncertainty and volatility to the bond's price and sensitivity to interest rate changes.