Supplementary Exercise 6.70 of IPS7e
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(a) The description does not give us any sense of what data may have
been involved. Let us for the sake of discussion assume that the
improvement is represented by a mean parameter mu. Then mu=0 would
correspond to no improvement, mu>0 would correspond to a positive
improvement and mu<0 would correspond to a worsening of the situation.
With this notation, the suggested test setup is
  H0: mu>0  versus  Ha: mu=0.

This is contrary to how statistical tests are being set up. The null
hypothesis must involve a specific value whereas the alternative
hypothesis can be one- or two-sided. The test should have been set up as
  H0: mu=0  versus  Ha: mu>0.


(b) The sample mean is a statistic, and hypotheses involve parameters, not
statistics. Therefore the description is totally wrong.

If the sample mean is our estimate of a population mean mu
(which is a parameter), the null hypothesis should have been phrased as
  H0: mu=value,
where value is some value relevant to the problem and not derived from
the data. The sample mean could by coincidence happen to be exactly equal 
to that value, in which case the test outcome will be non-significant. It
is however not meaningful to test a hypothesis stating that the
population mean equals the sample mean.


(c) Statistical significance is relative to a significance level, and
the most commonly significance level is 0.05. This means that P-values
less than 0.05 are statistically significant, and a P-value of 0.95 is
absolutely not significant.

Although there is some flexibility in setting the significance level, it
would never be set as high as 0.95. The idea of the significance level
is to single out events that could not have happened by chance alone. 
Events with a probability less than 0.95, say for example with a probability 
of 0.5, can easily happen by chance alone. In practice, the significance 
level is always close to zero.