A company that produces wireless headphones is testing a new battery for their products. In order to evaluate the capaci

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A company that produces wireless headphones is testing a new
battery for their products. In order to evaluate the capacity of
the new batteries, a sample of 50 headphones from a specific model
are equipped with the new battery and tested for autonomy. The
current average battery autonomy is 5.2 hours. Test results from
the sample of headphones equipped with the new battery produce a
sample mean of 5.6 hours and a sample standard deviation of 0.8
hours. For a significance level of 5%, can we conclude that the
autonomy of the new batteries is different from the autonomy of the
batteries currently in use?
a) Should this test for the mean be two-tailed,
right-tailed or left-tailed? Justify your answer. (5
points)
b) State the null hypothesis (5 points)
c) State the alternative hypothesis. (5 points)
d) Compute the p-value and comment on the result. (5
points)
e) Compute the rejection region (test statistic) and use it
to determine whether the null hypothesis should be rejected, for a
significance level of 5%. Do not forget to write a conclusion that
refers to the real-world problem, i.e. a conclusion that
people without a background in Statistics may understand. (5
points)
f) Could you have answered the previous question
(determining the test result for a significance level of 5%)
without computing the rejection region? Justify your
answer. (5 points)