The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage

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The desired percentage of SiO2 in a certain type
of aluminous cement is 5.5. To test whether the true average
percentage is 5.5 for a particular production facility, 16
independently obtained samples are analyzed. Suppose that the
percentage of SiO2 in a sample is normally
distributed with 𝜎 = 0.32 and
that x = 5.24. (Use 𝛼 =
0.05.)
(a) Calculate the test statistic and determine
the P-value. (Round your test statistic to two
decimal places and your P-value to four decimal
places.)
=
(b) If the true average percentage is 𝜇 = 5.6 and
a level 𝛼 = 0.01 test based
on n = 16 is used, what is the probability
of detecting this departure from H0?
(Round your answer to four decimal places.)
_______

(c) What value of n is required to
satisfy 𝛼 = 0.01 and 𝛽(5.6) = 0.01? (Round
your answer up to the next whole number.)
n = ______samples