An experimenter is concerned about radiation levels in her research laboratory. A room is only considered safe if the me

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An experimenter is concerned about radiation levels in her
research laboratory. A room
is only considered safe if the mean radiation level is 400 or less.
A random sample of
12 radiation measurements is taken at different locations in the
laboratory. These 12
measurements have a mean of 414 and a standard deviation of 17.
Radiation levels in
the lab are known to follow a normal distribution with standard
deviation 22. We would
like to conduct a hypothesis test at the 5% level of significance
to determine whether
there is evidence that the laboratory is unsafe.
1)The test statistic for the appropriate test of significance
is: (I know the answer is E)
(A) t = −2.20
(B) z = −2.20
(C) z = −2.85
(D) t = 2.85
(E) z = 2.20
2. What is the correct conclusion for the test? (I know the
answer is C but why?
(A) Reject H0. There is sufficient evidence that the lab is
safe.
(B) Fail to reject H0. There is insufficient evidence that the lab
is unsafe.
(C) Reject H0. There is sufficient evidence that
the lab is unsafe.
(D) Fail to reject H0. There is insufficient evidence that the lab
is safe.
(E) Reject H0. There is insufficient evidence that the lab is
unsafe.
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