How to do a science experiment to compare the transmission of Optic fibre and normal copper cables or wires?

You would need 2 computers, connected by exactly equal lengths of copper wire and fiber optic. To reduce the error from inexact measurement of the length, you should use extremely long lengths (several miles, ideally). Send the same data through both cables at the same time and measure and the time difference for when the data arrives.

It would be kind of difficult and expensive...

Buy (or borrow) a spool of, say, 110V, twin-lead lamp cord - the kind of lamp cord that electrical appliances are wired with...

If you can afford it - 250 ft or longer...

I say to use this because you could maybe reuse it in years to come...

Buy (or borrow) a spool of fiber optic cable...

Obtain a pulse generator capable of short (10 nanosecond would be great) pulses...

Obtain a dual trace oscilloscope...

Hook up a laser (bypass any power supply) to the pulse generator and send an optical signal down the fiber optical cable...

Hook up the end of the lamp cord spool to the same pulse generator output signal...

Detect the signal at the other end of the fiber with a very fast detector and put into channel 1 of the scope...

Take the signal at the other end of the lamp cord and put into channel 2 of the scope...

Compare the rise/fall times of the two signals as the pulse is narrowed...

There should be a slower rise/fall time for the lamp cord...

This is not an easy experiment...

There is a lot of detail I have left out - like how do you get the laser output into the end of the fiber optic so there is enough light to be detected at the other end...