If we reject the null hypothesis, h0: ρ = 0 , what can we conclude about the population correlation coefficient?

If the null hypothesis,  is rejected, then we can conclude that the correlation coefficient is significant. This means that there is enough evidence to conclude that a relationship exists between the two (or more) variables involved in the regression. 

Given is:

The initial height of the candle is 9 inches.

And rate of burning is 0.5 inches per hour.

Part A:

The ordered pairs are: {(0,9),(1,8.5),(2,8),(3,7.5),(4,7),(5,6.5)}

Here we will subtract 0.5 each time, with increasing the time per hour as the rate of burning is 0.5 inches per hour.

Part B:

Yes, it is a function because each x value has its own y value.

Part C:

Yes, the relation would still be a function. The only difference is the time, the candle reduces its height 0.45 inches per each hour so ordered pairs will be :  (0,9)  (1,8.55) (2,8.1)  (3,7.65)