find total power in circuit
Your calculations are correct. Since all the resistors are in series you can just add them up and that'll give you the total resistance, in your case 7kohm. 

Since everything is in series the current through the resistors will be the same 15.7mA. All that's left to do is to calculate the power dissipated by each resistor. Which you did calculate on the left hand side of the second page. So now just compare those calculated values with the values given on the schematic.

R1 rating is 0.5W and the power dissipated is 0.246W. Since 0.246W &lt; 0.5W therefore this rating is okay.

R2 rating is 0.25W and the power dissipated is 0.864W. Since 0.864W > 0.25W therefore this rating is not okay, use a 1W rating (ratings are standard)

R3 rating is 1W and the power dissipated is 0.619W. Since 0.619W &lt; 1W therefore this rating is okay.

R4 rating is 1W and the power dissipated is 0.123W. Since 0.123W &lt; 1W therefore this rating is okay.

I'm assuming when you said that: 


  "the power I calculated was less than the power on the circuit"


You mean that the power you calculated was less than the sum of the power ratings on the resistors in the circuit. The ratings on each resistor indicate how much power that resistor can dissipate (in terms of heat). It doesn't mean that the supply is going to deliver that amount of power to that resistor. 

As you can see by the equation you used for power:
\$P=I^2R\$
The power dissipated by the resistor is dependant on the current through it and the current through it is dependant on the resistor itself:
\$V=IR\$