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 were still true). As is stated also on slide
6L-4, the P-value expresses how surprising the observed outcome would be 
if H0 was 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.