Supplementary Exercise 6.142 of IPS7e
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The explanation is not correct.

Hypotheses are not true or false with certain probabilities, because
there is no randomness associated with a hypothesis being true or false
(according to the classical or 'frequentist' view of statistics; with 
the Bayesian view of statistics a different situation arises). The
hypothesis is a statement about the true population parameter(s), which 
are fixed (and unknown). Therefore, a statement like mu=4.8 is either true
or false, but this is a (fixed) fact of the true population.

The randomness is associated with our observations (our sample from the
population). A result being statistically significant at the 5% level
means that the chance of getting data like those we observed would be
at most 5% if the null hypothesis were true. The P-value is the
probability of getting data like those we observed by chance alone (that
is, if the null hypothesis and all other assumptions involved were true). 
As is stated also on slide 5L-15, the P-value expresses how surprising 
the observed outcome would be if H0 (and all the other assumptions) were true.

An essentially correct way of explaining statistically significant in a
similar format is (based on IPS 7e, Exercise 6.127):

A result being significant tells us that it cannot easily be
explained by chance alone.