Rather than carrying out IBP several times, let's establish a more general result. Let
One round of IBP, setting
gives
This is called a power-reduction formula. We could try solving for explicitly, but no need.
is small enough to just expand
as much as we need to.
Finally,
so we end up with
and the antiderivative is
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
<h3>What are the hypothesis tested?</h3>At the null hypothesis we test if the means are equal, hence:
At the alternative hypothesis, it is tested if they are different, hence:
For each sample, they are given as follows:
Hence, for the distribution of differences, they are given by:
The test statistic is given by:
In which is the value tested at the null hypothesis.
Hence:
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/13873630
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